Question

write a quadratic function with zeros 7 and -4. 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 $r_1=7$, $r_2=-4$, so:
$f(x)=(x-7)(x-(-4))=(x-7)(x+4)$

Step2: Expand the product

Use the FOIL method to multiply the binomials:
$f(x)=x\cdot x + x\cdot 4 -7\cdot x -7\cdot4$

Step3: Simplify to standard form

Combine like terms and simplify:
$f(x)=x^2 +4x -7x -28=x^2-3x-28$

Answer:

$x^2-3x-28$