Question

write a quadratic function with zeros 2 and 6. write your answer using the variable x and in standard form with a leading coefficient of 1. f(x) =

Explanation:

Step1: Use zero factor form

If a quadratic has zeros $r_1$ and $r_2$, it can be written as $f(x)=(x-r_1)(x-r_2)$. Here $r_1=2$, $r_2=6$, so:
$f(x)=(x-2)(x-6)$

Step2: Expand the binomials

Use the FOIL method: multiply first terms, outer terms, inner terms, last terms.

$$\begin{align*} f(x)&=x\cdot x - x\cdot6 -2\cdot x + (-2)\cdot(-6)\\ &=x^2 -6x -2x +12 \end{align*}$$

Step3: Combine like terms

Combine the linear terms $-6x$ and $-2x$.
$f(x)=x^2 -8x +12$

Answer:

$x^2 -8x +12$