Question

use $x^2 - 6x$ to answer the following questions.
$x = -\frac{b}{2a}$
use your value of $x$ in the equation to find the $y$-coordinate of the vertex.
$f(x) = a(x - h)^2 + k$

1. rewrite the quadratic in vertex form.

type a response

Explanation:

Step1: Identify a, b values

For $x^2 - 6x$, $a=1$, $b=-6$

Step2: Calculate vertex x-coordinate

Use $x=-\frac{b}{2a}$:
$x=-\frac{-6}{2(1)} = 3$

Step3: Find vertex y-coordinate

Substitute $x=3$ into $x^2 -6x$:
$y=(3)^2 -6(3)=9-18=-9$

Step4: Write vertex form

Use $f(x)=a(x-h)^2 +k$, where $(h,k)=(3,-9)$:
$f(x)=1(x-3)^2 -9$

Answer:

$f(x)=(x-3)^2 -9$