If (a,b)

is the vertex of f(x)=−5x^2−20x+10, then what is the value of b?

A. b=−10

B. b=−2

C. b=0

D. b=30

1 answer

To find the value of b when (a,b) is the vertex of f(x) = -5x^2 - 20x + 10, we know that the x-coordinate of the vertex is given by:

x = -b/(2a)

In this case, a = -5 and b = -20. Substituting these values into the formula, we get:

x = -(-20)/(2*(-5)) = 20/(-10) = -2

Now we can substitute x = -2 into the function f(x) to find the corresponding y-coordinate (b):

f(-2) = -5(-2)^2 - 20(-2) + 10
f(-2) = -5(4) + 40 + 10
f(-2) = -20 + 40 + 10
f(-2) = 30

Therefore, the value of b when (a,b) is the vertex of f(x) = -5x^2 - 20x + 10 is b = 30.

The correct answer is D. b = 30.