Question

What is the equation of the parabola that has a vertex at `(-15, -6)` and passes through point `(-19,7)`?

Answer 1

`y = 13/16 (x + 15 )^2 - 6`

Explanation:

The equation of a parabola in vertex form is :

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

where (h , k ) are the coordinates of the vertex.

equation is then : `y = a(x + 15 )^2 - 6`

Given the point (- 19 , 7 ) that lies on the parabola allows
substitution into the equation to find a .

using (- 19 , 7 ) : `7 = a(-19 + 15 )^2 - 6`

`7 = a(- 4 )^2 - 6 = 16a - 6`

so 16a = 7 + 6 = 13 `rArr a = 13/16`

equation of parabola is : `y = 13/16 (x + 15 )^2 - 6`