Question

write a quadratic function with zeros 3 and -9. 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 $r_1=3$, $r_2=-9$, so:
$f(x)=(x-3)(x-(-9))=(x-3)(x+9)$

Step2: Expand the binomials

Use the FOIL method: multiply first terms, outer terms, inner terms, last terms.
$f(x)=x\cdot x + x\cdot9 -3\cdot x -3\cdot9$

Step3: Simplify the expression

Combine like terms and compute constants:
$f(x)=x^2 +9x -3x -27=x^2+6x-27$

Answer:

$x^2+6x-27$