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

##### 1 Answer

Jan 22, 2016

# 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 #