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.

Answer 1

The vertex form of a parabola is given by:

y = a(x - h)^2 + k

where (h, k) is the vertex of the parabola.

Given that the vertex is (-8, -7), we can substitute these values into the equation we obtained earlier:

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

Simplifying:

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

Now, we can use the point (–7, –4) to find the value of "a":

-4 = a(-7 + 8)^2 - 7
-4 = a(1)^2 - 7
-4 = a - 7
a = -4 + 7
a = 3

Substituting this value back into the equation:

y = 3(x + 8)^2 - 7

Therefore, the equation of the parabola in vertex form is y = 3(x + 8)^2 - 7.