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Reil [10]
3 years ago
11

What is the vertex of the quadratic function f(x)=(x-6)(x+2)?

Mathematics
1 answer:
Nata [24]3 years ago
4 0

Answer:

(2, -16).

Step-by-step explanation:

(x - 6)(x + 2)

Convert to vertex form:

Expanding the parentheses we have:

x^2 + 2x - 6x - 12

= x^2 - 4x - 12

Completing the square:

= (x - 2)^2 - 4 - 12

= (x - 2)^2 - 16

So the vertex is (2, -16),

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Calculus help! Using the mean value theorem!
marta [7]
f is differentiable across its domain, so the MVT says there is some value of c in the open interval (a,b) such that

f'(c)=\dfrac{f(b)-f(a)}{b-a}

You have

f(x)=Ax^2+Bx+C\implies f'(x)=2Ax+B

so the equation above becomes

2Ac+B=\dfrac{(Ab^2+Bb+C)-(Aa^2+Ba+C)}{b-a}

Solve for c.

2Ac+B=\dfrac{A(b^2-a^2)+B(b-a)}{b-a}
2Ac+B=A(b+a)+B
2Ac=A(b+a)
c=\dfrac{b+a}2

so c is indeed the average of the endpoints, i.e. the midpoint.
8 0
3 years ago
Pleaseeeeee help I'll give Brainliest urgent!!!!!!!!!!!!!!!!!!!!
leonid [27]

Answer:

it is either 2 or 4

Step-by-step explanation: because if you break them apart you will get 2 or 4

5 0
3 years ago
Read 2 more answers
2 A change in the genes of a species over a<br> long period of time.
Blizzard [7]

Answer:

There is no question..?

3 0
3 years ago
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PLEASE HELP !!!!!!!
N76 [4]

Answer:

(B) Time (min) 2 , 3 , 7 , 9

Temperature (°C) 60.6 , 64.3 , 79.1 , 86.5

Step-by-step explanation:

The rate of change is found by using the formula for slope:

m=\frac{y_2-y_1}{x_2-x_1}

For option A, this gives us

m =(64.4-61.0)/(3-2) = 3.4/1 = 3.4

This is not more than relationship A.

For option B, we have

(64.3-60.6)/(3-2) = 3.7/1 = 3.7

This is more than relationship A.

For option C, we have

(65.3-61.8)/(3-2) = 3.5/1 = 3.5

This is not more than relationship A.

For option D, we have

(64.6-61.0)/(3-2) = 3.6/1 = 3.6

This is not more than relationship A.

7 0
3 years ago
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Please help<br> Complete the equation describing how<br> x and y are related.
djverab [1.8K]

Answer:

y = 5x + 3

Step-by-step explanation:

The answer that belongs in the ? is 5.

4 0
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