Practice!

Sample Problem

Write the standard form of the equation of the parabola that has a vertex (7, -1) and passes through the point (5, 15). Give your answers in whole numbers.

F(x)=(x-)2+

Solution

The standard form of the equation of any parabola whose vertex is (h, k) is:

f(x)=a(x-h)2+k

The vertex of this parabola is (7, -1)

f(x)=a(x-7)2-1

This parabola goes through the point (5, 15) so plug in x=5 and f(x)=15

15=a(5-7)2-1, 15=4a-1, 16=4a, 4=a

Therefore the equation of this parabola is:

F(x)=4(x-7)2+(-1)