Question

Consider the quadratic function:

f(x) = x2 – 8x – 9



Vertex: (StartFraction negative b Over 2 a EndFraction, f (StartFraction negative b Over 2 a))

What is the vertex of the function?

(
,
)

Answer 1

To find the vertex of the quadratic function \( f(x) = x^2 - 8x - 9 \), we can use the vertex formula:

\[
x = -\frac{b}{2a}
\]

For our function, the coefficients are:
- \( a = 1 \)
- \( b = -8 \)

Substituting the values into the formula gives:

\[
x = -\frac{-8}{2 \cdot 1} = \frac{8}{2} = 4
\]

Next, we need to find the corresponding \( y \) value by substituting \( x = 4 \) back into the function \( f(x) \):

\[
f(4) = (4)^2 - 8(4) - 9
\]
\[
= 16 - 32 - 9
\]
\[
= 16 - 32 - 9 = -25
\]

Thus, the vertex of the function is:

\[
(4, -25)
\]

So the final answer is:

\[
\boxed{(4, -25)}
\]