What is the equation of the parabola that has a vertex at $(3, -6)$ and passes through point $(-9,7)$ ?

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Answer 1 · 2018-03-05T21:37:55

$f(x)=13/144(x-3)^2-6$

We know that

$f(x)=a*(x-3)^2-6$

because of the vertex at $(3,-6)$ . Now we have to determinated $a$ by plugging in the point $(-9,7)$ .

$7=a*(-9-3)^2-6$

In order to find $a$ , we solve for $a$

$7=a*(-9-3)^2-6|+6$
$13=144a|:144$
$13/144=a~~0.09$

What is the equation of the parabola that has a vertex at (3, -6) (3, -6) and passes through point (-9,7) (-9,7) ?