# How do you write an equation of the parabola that passes through the point (2, 5) and has x-intercepts -2 and 4?

##### 1 Answer

Nov 20, 2016

There is a family of parabolas

#### Explanation:

graph{x^2-2x+8/5y-8=0 [-20, 20, -10, 10]}

graph{x^2+2xy+y^2-2x-37/5y-8=0 [-20, 20, -10, 10]}

The general second degree equation represents a parabola, when

the second degree terms form a perfect square.

Let the equation be

The parabola passes through (-2, 0), (4, 0) and (2, 5). So,

Solving this 3 X 4 system,

a = -2, c=-8 and b=8/5-4h-5h^2

See the answer.