The maximum or minimum of a quadratic function is found evaluating the polynomial at [tex]x = -\frac{b}{2\cdot a}[/tex].
A quadratic function is an algebraic function of the form:
[tex]y = a\cdot x^{2}+b\cdot x + c[/tex], [tex]\forall \,x, y, a, b, c\,\in \mathbb{R}[/tex] (1)
Where:
[tex]x[/tex] - Independent variable.[tex]y[/tex] - Dependent variable. [tex]a,\,b,\,c[/tex] - Coefficients.The maximum/minimum of a quadratic function is represented graphically by the vertex, which is the only point that has no a "twin" point by any means of symmetry. We can get the x-coordinate of the vertex by means of the quadratic formula:
[tex]a\cdot x^{2} + b\cdot x + (c- y) = 0[/tex] (2)
[tex]x = \frac{-b\pm \sqrt{b^{2}-4\cdot a\cdot (c-y)}}{2\cdot a}[/tex], where [tex]b^{2}-4\cdot a\cdot (c-y) = 0[/tex].
Hence, the x-coordinate of the vertex is:
[tex]x = -\frac{b}{2\cdot a}[/tex] (3)
And the y-coordinate of the vertex is determined by evaluating (1) at (3):
[tex]y = f\left(-\frac{b}{2\cdot a} \right)[/tex] (4)
The maximum or minimum of a quadratic function is found evaluating the polynomial at [tex]x = -\frac{b}{2\cdot a}[/tex].
We kindly invite to check this question on maxima and minima: https://brainly.com/question/12870574
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Answer: y = 2 (x+4)
Tim = alice + 4
Bob = tim x 2
Alice = x
y = 2 (x+4)
Bob (y), Alice (x), tim (x+4)
the movie theater offers a VIP member where you pay $75 for the VIP pass and then $4 per movie you see. People without the VIP pass that walk up to the movie theater pays $15 per movie they see
Answer:
so what are you trying to figure out
Step-by-step explanation:
Answer the question below
Answer:
Edit: Both are same.
Step-by-step explanation:
Volume is the total space occupied by an object.
Help Please!!
-5/k + 1 for k = -1
Answer:
6
Step-by-step explanation:
[tex]\frac{-5}{k} + 1\\\frac{-5}{-1} + 1\\5+1 = 6[/tex]
f(x) = 3x2 - 3x + 1 3х 1 Find f(-2)
Answer:
Assuming f(x) = 3x^2 - 3x + 1, f(-2) is 16.
Step-by-step explanation:
Check answer.
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A company ships bottles of olive oil to stores in boxes.
The graph shows a proportional relationship between
the number of boxes shipped and the number of
bottles of olive oil shipped. About how many bottles are
shipped in 8 boxes?
Answer:
about 110
Step-by-step explanation:
what is the ratio of 0.75 decimal
-5 or -15 whic one is bigger
Answer:
Step-by-step explanation:
-5 is bigger because it’s closer to 0 in a number line
Answer:
-5 because it is closer to 0 and -15 is farther away from 0 .
Step-by-step explanation:
tell whether the following sequence is geometric or not. If geometric find r
—
hi can someone please answer my question i really need the complete step-by-step solution. thank you ❤️
Answer:
this sequence is geometrical sequence
and it's formula is
[tex]y = a {r}^{n} \\ here \: a \: is \: first \: number \: is \: equal \: 1 \\ and \: the \: ratio \: is \: r \: is \: equal \: - 3 \\ y = 1 \times {( - 3)}^{n} [/tex]
PLEASE HELP, WILL GIVE BRAINLY!!!!!!
Given: 2PQ = PR
Prove: Q is the midpoint of line PR
Statement: 2PQ = PQ + QR
Reason: ???
Answer:
Given: 2PQ = PR
Prove: Q is the midpoint of line PR
Statement: 2PQ = PQ + QR
Step-by-step explanation:
If Q is the midpoint of PR then
PR = PQ + QR [by segment addition postulate]
2PQ = PR [given]
2PQ = PQ + QR
2PQ-PQ = PQ + QR-PQ [by subtracting PQ from both sides]
PQ = QR
[tex] \because[/tex] Q lies on PR and PQ = QR
[tex] \therefore[/tex] Q is the midpoint of PR
ayuda
encuentra el valor de la hipotenusa
Answer:
113. x = √65 cm
114. x= 7.10 cm
simplify. 5 - 8 ÷ 2 + 4
Answer:
5
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightStep-by-step explanation:
Step 1: Define
Identify
5 - 8 ÷ 2 + 4
Step 2: Simplify
Division: 5 - 4 + 4Subtract: 1 + 4Add: 5Which number sentence is true? O A) 2.3 x 102 > 2000 OB) 3.45 > 1-4.35| OC) 345 > 5:33 825 OD 13
Answer:
D) -2.14< root10 <|-2.8|
Step-by-step explanation:
the value for -2.14 is as plain as you can see, the negative version of 2.14.
The square root of 10 is 3.16227766.
The lines next to -2.8 is asking for the absolute value of -2.8, or the distance between that number and zero. The distance between -2.8 and 0 is positive 2.8, because distance can't be negative.
The 3 numbers taken from the explanations are -2.14, 3.16, and 2.8. Ranking them from least to greatest would give you -2.14, 2.8, 3.16, or -2.14< root10 <|-2.8|
What is 35% of the number 40?
Answer:
14
Step-by-step explanation:
convert 35% to a decimal by moving the decimal to the left two places
.35
.35 × 40 = 14
Answer:
87 percent
Step-by-step explanation:
You just simply divide percent you got (35) by the full amount you could get (40)
35 ÷ 40
Solve for P A= 2xP+4P
Answer: P = A/6
Step-by-step explanation: Isolate the variable by dividing each side by factors that don't contain the variable.
Show a different way to solve 25 x 28
Answer:
700=25x28
Step-by-step explanation:
The product of the two given numbers is 700.
The given expression is 25 × 28.
We need to find the product of these two numbers in different ways.
What is the distributive property of multiplication?The distributive property of multiplication over addition states that multiplying the sum of two or more addends by a number gives the same result as multiplying each addend individually by the number and then adding the products together. This property of multiplication over addition is used when we need to multiply a number by a sum.
Now, direct multiplication 25 × 28=700
Using distributive property we get 25 × (20+8)
=25 × 20 + 25 × 8
=500 + 200
=700
Therefore, the product of two given numbers is 700.
To learn more about the distributive property visit:
https://brainly.com/question/13130806.
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Find the perimeter of triangle ABC
Answer:
20 units
Step-by-step explanation:
to solve this equation you need the pythagorean theorem: a^2 + b^2 = c^2
2^2 + 7^2 = 53; square root of 53 is 7.28010989; or about 7.3 units (line AC)
2^2 + 6^2 = 40; square root of 40 is 6.32455532; or about 6.3 units (line BC)
4^2 + 5^2 = 41; square root of 41 is 6.40312424; or about 6.4 units (line AB)
7.3 + 6.3 + 6.4 = 20
20 units
