Question

find the vertex of the quadratic function given below.
$f(x) = (x - 4)(x + 2)$
a. $(1,-9)$
b. $(-1,9)$
c. $(4,-2)$
d. $(-4,2)$

Explanation:

Step1: Find x-intercepts

Set $f(x)=0$, solve $x-4=0$ and $x+2=0$:
$x=4$ and $x=-2$

Step2: Calculate vertex x-coordinate

Average the intercepts:
$x = \frac{4 + (-2)}{2} = \frac{2}{2} = 1$

Step3: Find vertex y-coordinate

Substitute $x=1$ into $f(x)$:
$f(1) = (1-4)(1+2) = (-3)(3) = -9$

Answer:

A. (1,-9)