Question

write a quadratic function with zeros 4 and -2. 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 $f(x)=(x-r_1)(x-r_2)$. Substitute $r_1=4$, $r_2=-2$:
$f(x)=(x-4)(x-(-2))=(x-4)(x+2)$

Step2: Expand the binomials

Use the FOIL method: $(a+b)(c+d)=ac+ad+bc+bd$
$f(x)=x\cdot x + x\cdot 2 - 4\cdot x - 4\cdot 2$

Step3: Simplify the expression

Combine like terms and simplify:
$f(x)=x^2 + 2x - 4x - 8 = x^2 - 2x - 8$

Answer:

$f(x)=x^2 - 2x - 8$