Question

write a quadratic function with zeros -9 and 7. write your answer using the variable x and in standard form with a leading coefficient of 1. g(x) =

Explanation:

Step1: Use zero-factor form

If $r_1$ and $r_2$ are zeros of a quadratic function, the function can be written as $g(x)=(x-r_1)(x-r_2)$. Here, $r_1=-9$ and $r_2=7$, so:
$g(x)=(x-(-9))(x-7)=(x+9)(x-7)$

Step2: Expand the binomials

Use the FOIL method $(a+b)(c+d)=ac+ad+bc+bd$:
$g(x)=x\cdot x + x\cdot(-7) + 9\cdot x + 9\cdot(-7)$

Step3: Simplify the expression

Combine like terms and compute constants:
$g(x)=x^2 -7x +9x -63=x^2+2x-63$

Answer:

$g(x)=x^2+2x-63$