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{{ printedBook.courseTrack.name }} {{ printedBook.name }} We want to write the equation of the parabola that passes through the point $(6,5)$ and has $x-$intercepts $1$ and $7.$

To do so, we will use the intercept 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−1)(x−7) $ Since the parabola passes through the point $(6,5),$ we can substitute $6$ for $x$ and $5$ for $y$ in the above equation, and solve for $a.$$y=a(x−1)(x−7)$

$5=a(6−1)(6−7)$

Solve for $a$

SubTermsSubtract terms

$5=a(5)(-1)$

DivEqn$LHS/5=RHS/5$

$1=a(-1)$

DivEqn$LHS/(-1)=RHS/(-1)$

$-1=a$

RearrangeEqnRearrange equation

$a=-1$