Question

Suppose a parabola has vertex (–8, –7) and also passes through the point (–7, –4). Write the equation of the parabola in vertex form.
a.y=(x+8)^2-7
b.y=3(x-8)^2-7
c.y=3(x+8)^2-7
d.y=3(x+8)^2+7

Answer 1

We have been given that a parabola has vertex $(-8,-7)$ and also passes through the point $(-7,-4)$. We are asked to write the equation of the parabola in vertex form.

We know that vertex form of parabola in format $y=a(x-h)^2+k$, where point (h,k) represents vertex of parabola.

Let us write equation of parabola using our given information as:

$y=a(x-(-8))^2-7$

$y=a(x+8)^2-7$

Now we will substitute the coordinates of point  $(-7,-4)$ to solve for a as:

$-4=a(-7+8)^2-7$

$-4=a(1)^2-7$

$-4=a-7$

$-4+7=a-7+7$

$3=a$

Therefore, our required equation would be $y=3(x+8)^2-7$ and option 'c' is the correct choice.