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{{ printedBook.courseTrack.name }} {{ printedBook.name }} We want to write the equation of the parabola that passes through the point $(8,-2)$ and has $x-$intercepts $6$ and $10.$

To do so, we will use the factored form of a quadratic function. $y=a(x−p)(x−q) $ In this form, $p$ and $q$ are the $x-$intercepts. Therefore, we can partially write our equation. $y=a(x−6)(x−10) $ Since the parabola passes through the point $(8,-2),$ we can substitute $8$ for $x$ and $-2$ for $y$ in the above equation, and solve for $a.$$y=a(x−6)(x−10)$

$-2=a(8−6)(8−10)$

Solve for $a$

SubTermsSubtract terms

$-2=a⋅2(-2)$

DivEqn$LHS/(-2)=RHS/(-2)$

$1=a⋅2$

DivEqn$LHS/2=RHS/2$

$21 =a$

RearrangeEqnRearrange equation

$a=21 $