Question

Write an equation for a parabola with x-intercepts (-3,0) and (5,0) which passes through the point (4, -21).

Answer 1

The equation of a parabola can be express as follows

`\begin{gathered} y=a(x-p)(x-q) \\ y=a(x+3)(x-5) \\ x=4 \\ y=-21 \\ -21=a(4+3)(4-5) \\ -21=a*7*-1 \\ -21=-7a \\ a=3 \end{gathered}`

Therefore,

`\begin{gathered} substitute\text{ for a} \\ y=a(x-p)(x-q) \\ y=3(x+3)(x-5) \end{gathered}`