Write an equation for the parabola that passes through (4, 3) and has x-intercepts of −1 and 5.

Answer 1

Equation has the form y = a(x-h)² + k, where (h,k) is the vertex..

The x-coordinate of the vertex lies halfway between the x-intercepts. So, h = 2.

y = a(x-2)² + k

Since the points (4,3) and (-1, 0) are on the graph, we obtain the system of equations:

4a + k = 3

9a + k = 0

Subtract the equations to get -5a = 3. So, a = -3/5.

Then, -27/5 + k = 0

k = 27/5

Equation: y = (-3/5)(x-2)² + 27/5.