Another Math Problem

Question

Determine the equation of the parabola with vertex

(-2,5) and that passes through (4,-8)

Answer 1

We know a parabola takes the form y = a(x – h)² + k, where the vertex is at (h, k). Plugging in our known vertex coordinates of (-2,5) and our known point (4, -8) we can solve for a:

1. y = -8
2. a = unknown
3. x = 4
4. h= -2
5. k = 5
6. -8 = a*(4-(-2))²+5 --> -8 = a*(6)²+5 --> -8 = 36*a + 5
7. Isolate the variable a, so that 36*a = -13
8. divide both sides by 36 to solve for a = -13/36 = -1/3

Plugging a, h and k back into our parabolic equation we end up with:

1. y = -1/3*(x +2)² + 5