Answer: -1536
Step-by-step explanation:
1: 4(3+3) (3+1) (3+5) (3-5)
2: 4(6) (4) (8) (-2)
3: 24 (4) (8) (-2)
4: 96 (8) (-2)
5: 768 (-2)
= -1536
which value of x is a solution...
Answer:
(4), -5/6
Step-by-step explanation:
[tex]13-36x^2-13=-12-13\\-36x^2=-25\\\frac{-36x^2}{-36}=\frac{-25}{-36}\\x^2=\frac{25}{36}\\x=\sqrt{\frac{25}{36}},\:x=-\sqrt{\frac{25}{36}}[/tex]For x^2 = f(a), x = f(a), -f(a)
[tex]x=\sqrt{\frac{25}{36}},\:x=-\sqrt{\frac{25}{36}}\\\sqrt{\frac{25}{36}}\\\sqrt{25}\\\sqrt{5^2}=5\\=\frac{5}{\sqrt{36}}\\\sqrt{36}\\=\sqrt{6^2}=6\\=\frac{5}{6}[/tex]
Reverse the same equation from the negative side
[tex]=-\frac{\sqrt{25}}{\sqrt{36}}\\\sqrt{25}\\=\sqrt{5^2}\\=5\\=-\frac{5}{\sqrt{36}}\\\sqrt{36}\\=\sqrt{6^2}\\=6\\=-\frac{5}{6}[/tex]
Therefore,
[tex]x=\pm\frac{5}{6}[/tex]
Someone please help me
Answer:
Please see the picture below. You were on the right track. You were just off in letter A.
Step-by-step explanation:
a² + b²
______
a-b
if a = -3 and b = -5
Answer: -17
Step-by-step explanation:
-3^2 + -5^2/ -3 - (-5)
-34 / -3 - (-5)
-34/2
-17
22 17 25 41 39 4
Work out the difference between the two prime numbers in the list above.
The difference between the two prime numbers 17 and 39 is 22.
What are referred as the prime numbers?Prime numbers are those who have only two factors: 1 and the number on its own.
A prime number is a number greater than one with precisely two factors, i.e., 1 as well as the number itself. For example, the number 7 has only two factors: 1 and 7. As a result, it is a prime number. However, the number 6 has four factors: 1, 2, 3, and 6. It is a composite numbers.A prime number is one that is the whole number larger than one.It has only two factors: 1 and the number it's own.There's only the one even prime number: 2.Such a two prime numbers always are co-prime numbers.Every number can be represented as a prime number product.For the number given:
22 17 25 41 39 4
The two primes numbers are 17 and 39.
The difference is 39 - 17 = 22.
Thus, the difference between the two prime numbers is 22.
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express [tex]\frac{5x^{2} +20x+16}{x(x+1)^{2} }[/tex] in partial fractions
Answer:
[tex]\dfrac{5x^2+20x+16}{x(x+1)^2} & \equiv \dfrac{16}{x}-\dfrac{11}{(x+1)}-\dfrac{1}{(x+1)^2}[/tex]
Step-by-step explanation:
When writing an algebraic fraction as an identity, if its denominator has repeated linear factors, the power of the repeated factor indicates how many times that factor should appear in the partial fractions.
Write out the fraction as an identity:
[tex]\begin{aligned}\dfrac{5x^2+20x+16}{x(x+1)^2} & \equiv \dfrac{A}{x}+\dfrac{B}{(x+1)}+\dfrac{C}{(x+1)^2}\\\\\implies \dfrac{5x^2+20x+16}{x(x+1)^2} & \equiv \dfrac{A(x+1)^2}{x(x+1)^2}+\dfrac{Bx(x+1)}{x(x+1)^2}+\dfrac{Cx}{x(x+1)^2}\\\\\implies 5x^2+20x+16 & \equiv A(x+1)^2+Bx(x+1)+Cx\end{aligned}[/tex]
Calculate the values of A and C using substitution:
[tex]\begin{aligned}\textsf{When }x=0 \implies 16 & =A(1)+B(0)+C(0) \implies A=16\\\\\textsf{When }x=-1 \implies 1 & =A(0)+B(0)+C(-1) \implies C=-1\end{aligned}[/tex]
Substitute the found values of A and C and expand the identity:
[tex]\begin{aligned}\implies 5x^2+20x+16 & \equiv 16(x+1)^2+Bx(x+1)-x\\& \equiv 16x^2+32x+16+Bx^2+Bx-x\\& \equiv (16+B)x^2+(31+B)x+16\\\end{aligned}[/tex]
Compare the coefficients of the x² term to find B:
[tex]x^2 \textsf{ term } \implies 16+B =5\implies B & =-11[/tex]
Replace the found values of A, B and C in the original identity:
[tex]\dfrac{5x^2+20x+16}{x(x+1)^2} & \equiv \dfrac{16}{x}-\dfrac{11}{(x+1)}-\dfrac{1}{(x+1)^2}[/tex]
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solve the question 3/8x-1/4=1/2
x=?
Answer:
Step-by-step explanation:
the answer is simply 2
Ricky has some cookies. he ate 1/8 of his cookies and an additional 14 cookies on friday. he then ate 3/10 of the remaining cookies and an additional 24 cookies on saturday. he ate 40 cookies on sunday and had 34 cookies left. how many cookies did ricky have at first?
Ricky had 176 cookies initially
Let Ricky has x number of cookies
Cookies left after he ate 1/8 of his cookies and additional 14 cookies:
x - (1/8x + 14)
Cookies left after he ate 3/10 of the remaining cookies and an additional 24 cookies on Saturday:
x - (1/8x + 14) - 3/10(x - (1/8x + 14)) + 24)
Cookies left after he ate 40 more cookies on Sunday
x - (1/8x + 14) - 3/10(x - (1/8x + 14)) + 24) - 40 ------(1)
Cookies left with him at the end = 34
Therefore, equating equation (1) with 34
(7/10)((7x/8) - 14) - 64 = 34
x = 176
Thus Ricky had 176 cookies intially
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find the product of the next two numbers in the sequence.
-27,-17,-13,-9, _ , _
Answer:
-5,-1
Step-by-step explanation:
add 4 to get the next number
Use the following items to determine the total assets, total liabilities, net worth, total cash inflows, and total cash outflows.
Rent for the month $ 1,390 Monthly take-home salary $ 3,920
Cash in checking account $ 1,340 Savings account balance $ 2,770
Spending for food $ 1,110 Balance of educational loan $ 3,050
Current value of automobile $ 8,020 Telephone bill paid for month $ 85
Credit card balance $ 334 Loan payment $ 143
Auto insurance $ 321 Household possessions $ 3,510
Stereo equipment $ 3,320 Payment for electricity $ 189
Lunches/parking at work $ 204 Donations $ 116
Home computer $ 2,490 Value of stock investment $ 1,160
Clothing purchase $ 139 Restaurant spending $ 223
i need help with this
The answer will be : x = -- 3y -- 9
⇒ -2 (x + 3y) = 18
⇒ -(2x + 2 * 3y) = 18
⇒ -(2x + 6y) = 18
⇒ (-2x -6y) + 6y = 18 + 6y
⇒ -2x -6y + 6y = 6y + 18
⇒ -2x = 6y + 18
⇒ [tex]\frac{2x}{2} = \frac{-6y + 18}{2}[/tex]
⇒ [tex]x = \frac{-(2*3)y + (2*3)^{2} }{2}[/tex]
⇒ [tex]\frac{-2*3\frac{2*3y}{2*3} + \frac{(2*3)^{2} }{2*3} }{2}[/tex]
⇒ [tex]x = \frac {2*3(y + (3)^{2 - 1}) }{2}[/tex]
⇒ [tex]x = \frac{-2*3(y + 3)}{2}[/tex]
⇒ x = -[3(y + 3)]
⇒ x = (3y + 3*3)
⇒ x = -(3y + 9)
⇒ x = - 3y - 9
WORKING NOTES :
-2 (x + 3y) = 18
[We must multiply a term and an expression in order to enlarge this word.
We'll utilize the following product distributive property:
A(B + C) = AB + AC
⇒ -(2x + 2 * 3y) = 18
The final expression, in this case, will have two terms:
The first term is a product of '2' and 'x'
the second term is a product of '2' and '3y'.]
In this term, numerical components have been multiplied.
⇒ -(2x + 6y) = 18
We must group all the variable terms on one side of the equation and all the constant terms on the other in order to solve this linear equation.
⇒ (-2x -6y) + 6y = 18 + 6y
Here, the '-' (minus) term, -6y will be moved to the right side.
When a term "moves" from one side of the equation to the other, you'll notice that its sign changes.
Parentheses around expressions must be eliminated.
Each term in the expression changes sign if a negative sign is placed in front of it. Otherwise, the expression stays the same.
There is no negative sign in the situation.
⇒ -2x -6y + 6y = 6y + 18
In order to join like terms in this expression, we must first sum all of the numerical coefficients and, if necessary, replicate the literal section.
Nothing in a number suggests a value of 1.
There is just one set of related terms: -6y, 6y.
⇒ -2x = 6y + 18
We must eliminate the coefficient that multiplies the variable in this linear equation in order to isolate it.
If both sides are divided, then the coefficient must be removed (-2)
⇒ [tex]\frac{2x}{2} = \frac{-6y + 18}{2}[/tex]
We must simplify this fraction to its simplest form.
To do this, divide the variables that occur in both the numerator and the denominator.
The common factor, in this case, is 2.
⇒ [tex]x = \frac{-(2*3)y + (2*3)^{2} }{2}[/tex]
We must consider the GCF (Greatest Common Factor).
The GCF and the original expression, split by the GCF, provide the final term.
⇒ [tex]\frac{-2*3\frac{2*3y}{2*3} + \frac{(2*3)^{2} }{2*3} }{2}[/tex]
GCF in this case is 2*3.
The fraction [tex]\frac{2*3y}{2*3}[/tex] must be lowered to its simplest form. To do this, divide the variables that occur in both the numerator and the denominator.
Here, the common factor is 2*3.
⇒ [tex]x = \frac {2*3(y + (3)^{2 - 1}) }{2}[/tex]
The expression must be lowered to its simplest form.
Driving out the components that exist in both the numerator and the denominator will accomplish this.
2*3 is a common factor.
⇒ [tex]x = \frac{-2*3(y + 3)}{2}[/tex]
Numerical terms in the factor {y + (3²⁻¹)} is added which makes it (y + 3)
The fraction will then be broken down into its smallest terms next.
To do this, divide the variables that occur in both the numerator and the denominator.
2 is the common factor.
⇒ x = -[3(y + 3)]
⇒ x = -(3y + 3*3)
We must multiply a term and an expression in order to expand this term.
We'll utilize the following product distributive property:
A=AB+AC = A(B + C)
The final expression, in this case, will have two terms:
"3" and "y" are the product in the first term.
The second term is the result of the numbers 3 and 3.
⇒ x = -(3y + 9)
This term's numerical terms have been multiplied by three (3*3 = 9).
⇒ x = - 3y - 9
The parenthesis around expressions must be eliminated.
Each term in the expression changes sign if a negative sign is placed in front of it.
Otherwise, the expression stays the same.
The signs of the following two terms will now change. -(3y + 9) = - 3y - 9
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Use cross products to solve the proportion.
StartFraction 4 over 3 EndFraction = StartFraction x over 12 EndFraction
1. Use cross products: (4)(12) = 3x
2. Multiply: 48 = 3x
3. Divide both sides by 3:
= x
drawing.
According to the cross product, The value of x in the expression becomes 16.
According to the statement
We have to find that the value of the expression.
So, For this purpose, we know that the
Cross product is a binary operation on two vectors in three-dimensional space.
From the given information:
The expression is a
StartFraction 4 over 3 EndFraction = StartFraction x over 12 EndFraction
IN simple words, it becomes:
4/3 = x/12
Then we have to find the value of the x then
4/3 = x/12
Now cross multiply each other then
4 =3x/12
3x = 48
Then
x = 48/3
x = 16.
So, According to the cross product, The value of x in the expression becomes 16.
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5 times the quanity x increased by seven, minus
4 Cubed
The mathematical expression can be written as [tex]5(x+7)-4^3[/tex]
Any combination of terms that have undergone operations like addition, subtraction, multiplication, division, etc. is known as an algebraic expression (or variable expression). Let's use the equation 5x + 7 as an example. Thus, 5x + 7 is an illustration of an algebraic expression.
We frequently have to understand a written phrase in order to write an expression. For instance, the notation x + 6 can be used to represent the phrase "6 added to some number," where x stands for the unknown value.
The algebraic properties most frequently utilized to simplify algebraic statements are associative, commutative, and distributive.
Here the quantity x is increased by 7 and the sum is multiplied by 5.
so we get 5(x+7).
Now 4 cubed is subtracted from the resulting expression.
Therefore the expression looks like [tex]5(x+7)-4^{3}[/tex] .
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what is the equation in point-slope form of the line passing through (0, 5) and (−2, 11)? (1 point) y − 5
y - 11 = -3 ( x + 2) is the equation in point-slope form of the line .
What is slope ?
The inclination of a line with respect to the horizontal is measured numerically. The ratio of the vertical to the horizontal distance between any two points on a line, ray, or line segment is known as its slope in analytic geometry ("slope equals rise over run").Given points : (0, 5) and (−2, 11)
Slope of the line passing through given points
[tex]m = \frac{y_{2}- y_{1} }{x_{2} - x_{1} } = \frac{11 - 5}{-2 - 0} = \frac{6}{-3} = -3[/tex]
Thus, slope of line passing through given points m=-3
We know that the equation of a line passing through points ( x₀ , y₀) with slope 'm' is ( y - y₀ ) = m(x - x₀)
Thus, equation of a line passing through (−2, 11) with slope m=-3 will be
( y - 11 ) = -3 ( x - (-2))
y - 11 = -3 ( x + 2)
Hence, the equation of line is y - 11 = -3 ( x + 2).
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Help please this is kinda hard and important for me.
Applying the angle relationship, the measures of the angles are:
m<a = 126°
m<b = 54°
m<c = 126°
m<d = 54°
m<e = 126°
m<f = 54°
m<g = 126°
What are Angles formed by Transversal and Parallel Lines?The diagram shows different angles that are formed when a transversal crosses two parallel lines. To find the measure of the missing angles, we would apply the angle relationship.
m<a = 180 - 54 [linear pair]
m<a = 126°
m<b = 54° [vertical angles pair]
m<c = m<a [vertical angles pair]
m<c = 126°
m<d = 54° [corresponding angles]
m<e = m<a [corresponding angles]
m<e = 126°
m<f = m<d [vertical angles pair]
m<f = 54°
m<g = m<e [vertical angles pair]
m<g = 126°
Therefore, applying the angle relationship, the measures of the angles are:
m<a = 126°
m<b = 54°
m<c = 126°
m<d = 54°
m<e = 126°
m<f = 54°
m<g = 126°
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8.) What is the circumference of a circle?
It is the perimeter of the circle?
It is the area of the circle?
Answer:
[tex]\large\boxed{\textsf{The Circumference is the Perimeter of the circle.}}[/tex]
Step-by-step explanation:
[tex]\textsf{We are asked to identfy what the Circumference is.}}[/tex]
[tex]\Large\underline{\textsf{What is the Circumference?}}[/tex]
[tex]\textsf{The Circumference is a fancy word to describe the sum of the arcs of a circle.}[/tex]
[tex]\textsf{The total of the area 'on' the circle is commonly referred to as the Perimeter.}[/tex]
[tex]\mathtt{Circumference = (diameter)\pi }[/tex]
(-1)X 12 times=(-1) to the 12th power. Will these products be negative or positive?
[tex](-1)x\times(-1)^{12}\implies -x\times(-1)^{2+2+2+2+2+2} \\\\\\ -x\times(-1)^2 (-1)^2 (-1)^2 (-1)^2 (-1)^2 (-1)^2 \implies -x\times 1\cdot 1\cdot 1\cdot 1\cdot 1\cdot 1\implies -x[/tex]
bear in mind that any value raised to an even power, will always positivize.
[tex]\frac{8(29-7*4)}{4+7-8+1}-3(2)/6[/tex]
The solution for the expression {8 ( 29 - 7 * 4 ) / ( 7 + 4 - 8 + 1 } - 3 ( 2 ) / 6 will be 1.
We are given the expression:
{8 ( 29 - 7 * 4 ) / ( 7 + 4 - 8 + 1 } - 3 ( 2 ) / 6
We will solve this expression by using the property of PEMDAS:
Solving the expression , we get
{8 (29 - 28) / 11 - 8 + 1} - 3 (2) / 6
= (8 × 1) / 4 -( 6 / 6)
= 2 - 1
= 1
Therefore, the solution for the expression {8 ( 29 - 7 * 4 ) / ( 7 + 4 - 8 + 1 } - 3 ( 2 ) / 6 will be 1.
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Aaron is helping his uncle plant an apple orchard. After picking up a truckload of trees, they plant 12 of them. The next day, they still have 40 trees left to plant. Which equation can you use to find the total number of trees n in the original truckload?
A new apple orchard is being planted by Aaron's uncle. They plant 12 trees after picking up a truckload of them. They still need to plant 40 trees the following day.
The letter (N) is the symbol used to represent natural numbers. Natural numbers are also known as counting numbers, and they begin with the number 1 and continue to infinity (never ending), which is represented by three dots (...)
900n - 9[tex]n^2[/tex] = A(n) = n(900 - 9n)
For the highest A(n), A'(n) = 0, A'(n) = 900 - 18n = 0, 18n = 900, and n = 900/18 = 50.
50 trees should be planted per acre to produce the most apples possible
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darren drives to school in rush hour traffic and averages . he returns home in mid-afternoon when there is less traffic and averages . what is the distance between his home and school if the total traveling time is ?
1 hour & 45 minutes is the distance between his home and school.
What is distance short answer?
Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.d=rt
distance = rate of speed times time
d= 33X = 44(7/4-X)
33X = 77- 44X
77X = 77
X = 1 hour
33X = 33 miles
44(7/4 - 4/4) = 33 miles each way
1 hour & 45 minutes = 1 3/4 hours or 7/4 hours
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The infant has apgar scores of 7 at 1 minute and 9 at 5 minutes. what is the indication of this assessment finding?
An infant may have had birthing complications that reduced the amount of oxygen in her blood if her Apgar score ranges from 7 at 1 minute to 9 at 5 minutes. In this situation, the hospital nurses will most likely vigorously dry her with a towel while holding oxygen under her nose.
What are Apgar scores?The Apgar score is a recognized and practical way to report on the newborn baby's condition right after birth and their reaction to resuscitation, if necessary. One's particular neonatal mortality or neurologic prognosis cannot be predicted by the Apgar score alone, nor can it be regarded as a result of suffocation. It should also not be utilized to do so. An infant's spontaneous breathing score and the Apgar score given after resuscitation are not the same thing. An enhanced Apgar score reporting form that takes into account concurrent resuscitative treatments is encouraged by both the American Academy of Pediatrics and the American College of Obstetricians and Gynecologists.
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Create a very long sentence with at least four phrases using only three propositions. identify the propositions and create logic sentences.
(q ∨ (¬r ∧ ¬q)) → ¬p is the propositions and create logic sentences.
What is propositions ?
An axiom is a mathematical assertion that is predicated on a proposition, such as "3 is greater than 4," "an infinite set exists," or "7 is prime."
If you are more than 18 years old or if you are above 18 but lack identification proving your age, you are not permitted to to watch cartoon.
Prepositions -
p = You are allowed to watch cartoon.
q = your age is more than 18 years old
r = you have age proof
(q ∨ (¬r ∧ ¬q)) → ¬p
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Which equation is true when c = 3?
2c + 8 = 31
35 − 5c = 32
9 − 6c = 0
4c + 8 = 20
Answer:
4c + 8 = 20
Step-by-step explanation:
To find which equation is true, we have to plug 3 into x in each equation.
2c + 8 = 31
Plug in 3 into c
2(3) + 8 = 31
6 + 8 = 31
14 = 31
Since 14 doesn't equal 31, this equation isn't true.
35 − 5c = 32
Plug in 3 into c
35 − 5(3) = 32
35 - 15 = 32
20 = 32
Since 20 doesn't equal 32, this equation isn't true.
9 − 6c = 0
Plug in 3 into c
9 − 6(3) = 0
9 − 18 = 0
-9 = 0
Since -9 doesn't equal 0, this equation isn't true.
4c + 8 = 20
Plug in 3 into c
4(3) + 8 = 20
12 + 8 = 20
20 = 20
Since 20 equals 20, this equation is true.
Have a lovely rest of your day! :)
Graph the equation. Plot at least five points on the graph and label them with their
coordinates.
3. (-1,-2), (0,-1), (1,0), (2,1), and (3,2)
3. (0,0), (-1,2), (1,2), (-2,4), and (2,4)
EASY NEED THE ANSWER FAST
b: 3 x 10 to the power of 7
can you please give brainliest
[(2 + 4 × 2) − 5]3.
PLEASE HELP ME AND PLEASE EXPLAIN HOW YOU GOT THE ANSWER
[tex] \large \bf \implies{15}[/tex]
Step-by-step explanation:[tex]\bf \longrightarrow((2 + 4 \times 2) - 5) \times 3[/tex]
Step 1) ; Calculate the product or quotient
[tex]\bf \longrightarrow((2 + 8) - 5) \times 3[/tex]
Step 2) ; Calculate the sum or difference
[tex]\bf \longrightarrow(10 - 5) \times 3[/tex]
Step 3) : Calculate the sum or difference
[tex]\bf \longrightarrow5 \times 3[/tex]
Step 4) : Calculate the product or quotient
[tex]\bf \longrightarrow15[/tex]
solve 12n + 7p - 6n = 25p for n
Answer:
n = 3p
Step-by-step explanation:
12n + 7p - 6n = 25p
12n - 6n +7p = 25p
12n - 6n = 25p - 7p
6n = 18p
[tex]n=\frac{18p}{6}[/tex]
n = 3p
HELPPP
Solve for x and graph the solution on the number line below.
-x - 8 ≤ -15 and -18 ≤ -x - 8
The Solution in inequality form is 7 ≤ x ≤ 10.
The Solution in interval notation: [7,10].
What is the solution to the compound inequality?Given the data in the question;
-x - 8 ≤ -15 and -18 ≤ -x - 8
To solve, simplify the first part of the inequality by solving for x.
-x - 8 ≤ -15
Add 8 to both sides
-x - 8 + 8 ≤ -15 + 8
-x ≤ -7
Divide both sides by -1
Note that when dividing both sides of an inequality by a negative value, the inequality sign flips direction.
-x/-1 ≥ -7/-1
x ≥ 7
Next, simplify the second part of the inequality by solving for x
-18 ≤ -x - 8
Rewrite as
-x - 8 ≥ -18
Add 8 to both side
-x - 8 + 8 ≥ -18 + 8
-x ≥ -10
Divide both sides by -1
Note that when dividing both sides of an inequality by a negative value, the inequality sign flips direction.
-x/-1 ≤ -10/-1
x ≤ 10
Now, the intersection consist of the elements that are contained in both intervals.
The Solution in inequality form is 7 ≤ x ≤ 10.
The Solution in interval notation: [7,10].
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For the function g defined above, a is a constant and g(4)=8. What is the value of g(-4)?
The value of g(-4) is 8.
A set of inputs and outputs that are connected to one another in some way is referred to as a relation. We refer to the relations as a function when each input results in a single output. However, you must be certain that no input leads to more than one output in order to determine if a relation is a function or not.
Only when each element of a nonempty set M has a single range to a nonempty set N is a function a relation.
g(x) = ax^2 + 24
⇒ g(4) = a (4)^2 + 24
⇒ 8 = 16a + 24
⇒ 8 − 24 = 16a
⇒ −16 = 16a
⇒ a = −1
Since, g(−4) = a(−4) ^2 + 24
∴ g(−4) = 16(−1) + 24
⇒ g(−4) = 8
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In the figure below, m1=3x° and m2 = (x+18)°.
Find the angle measures.
L
2
m 21 =
m2 2 =
Answer: m 21=
I got it right on test!
Step-by-step explanation:
WILL GIVE THE BRAINLIEST
A graph of a quadratic function is shown. Use the graph for questions 1 through 4.
1. Use the graph to determine the value of for the function.
2. Write the equation of the parabola in vertex form.
3. Convert the vertex form of the parabola to standard form.
4. Use standard form of the parabola to identify the y-intercept of the function.
5. The factored form of a quadratic function is represented by () = 2(―4)(―6).
Write the equation in standard form.
For questions 6 through 9, a graph and table of values for () are shown.
6. Use the table or the graph to determine the value of for the function.
7. Write the equation in vertex form.
8. Write the equation in factored form.
9. Write the equation in standard form.
10. The function () is represented by () = 2(+ 3)^2 +4. Rewrite the function in
standard form.
The points where the graph intercepts the x-axis is the root of the function.
from the graph the points are 3.9 and 6.1
How to write the equation of the parabola in vertex formThe vertex v is at v ( 5, -4 ) this is equivalent to v ( h, k )
the equation of parabola in vertex form is y = a ( x- h )^2 + k
y = a ( x - 5 )^2 + {-4)
substituting point ( 4, -1 ) from the graph we have:
-1 = a ( 4 - 5 )^2 - 4
-1 = a - 4
a = 3
substituting the known values to y = a ( x- h ) + k
y = 3 ( x - 5 )^2 - 4
How to write the equation of the parabola in factored formy = 3 ( x - 5) ( x - 5 ) - 4
How to write the equation of the parabola in standard formy = 3 ( x - 5) ( x - 5 ) - 4
y = 3 ( x^2 - 10x + 25 ) - 4
y = 3x^2 - 30x + 75 - 4
y = 3x^2 - 30x + 71
Graph BHow to find the roots of the the function
The points where the graph intercepts the x-axis is the root of the function.
from the graph the points are 2 and 4
How to write the equation of the parabola in vertex form
The vertex v is at v ( 3, 2 ) this is equivalent to v ( h, k )
the equation of parabola in vertex form is y = a ( x- h )^2 + k
y = a ( x - 3 )^2 + 2
substituting point ( 0, -16 ) from the graph we have:
-16 = a ( 0 - 3 )^2 + 2
-16 = a - 9 + 2
-16 = a - 7
a = -9
substituting the known values to y = a ( x- h ) + k
y = -9 ( x - 3 )^2 + 2
How to write the equation of the parabola in factored formy = -9 ( x - 3) ( x - 3 ) + 2
How to write the equation of the parabola in standard formy = -9 ( x - 3) ( x - 3 ) + 2
y = -9 ( x^2 - 6x + 9 ) - 4
y = 3x^2 - 54x - 81 - 4
y = 3x^2 - 54x - 85
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