 # The factored form of a quadratic function is f(x)=(x‒p)(x‒q). amanf 2021-02-03 Answered

The factored form of a quadratic function is $f\left(x\right)=\left(x‒p\right)\left(x‒q\right)$. The standard form of a quadratic function is $f\left(x\right)=a{x}^{2}+bx+c$. The factored form for a quadratic function tells us the x-intercepts of the quadratic function, while the standard form for a quadratic function tells us the y-intercept of the quadratic function.
If $p=2$ and $q=-3$, use what you have learned about multiplying polynomials to
- write the factored form of the quadratic function f(x)
- write the standard form for the quadratic function f(x)

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Factored form of the quadratic function f(x) is
$f\left(x\right)=\left(x-p\right)\left(x-q\right)$
put $p=2,q=-3$
$=\left(x-2\right)\left(x-\left(-3\right)\right)$
$f\left(x\right)=\left(x-2\right)\left(x+3\right)\right)$
Standart form of a quadraticfunction is $f\left(x\right)=\left(x-2\right)\left(x+3\right)$
$=x\left(x+3\right)-2\left(x+3\right)$
$={x}^{2}+3x-2x-6$
$f\left(x\right)={x}^{2}+x-6$