Question

What is the equation of a quadratic function whose graph passes through (-3,0) (4,0) and (1,24)? Write your equation in standard form.

Answer 1

`y=-2x^2+2x+24`

Explanation:

Well given the standard form of a quadratic equation:

`y=ax^2+bx+c`

we can use your points to make 3 equations with 3 unknowns:

Equation 1:
`0=a(-3)^2+b(-3)+c`
`0=9a-3b+c`

Equation 2:
`0=a4^2+b4+c`
`0=16a+4b+c`

Equation 3:
`24=a1^2+b1+c`
`24=a+b+c`

so we have:

1) `0=9a-3b+c`
2) `0=16a+4b+c`
3) `24=a+b+c`

Using elimination (which I assume you know how to do) these linear equations solve to:

`a = -2, b = 2, c = 24`

Now after all that elimination work put the values into our standard quadratic equation:

`y=ax^2+bx+c`

`y=-2x^2+2x+24`

graph{-2x^2+2x+24 [-37.9, 42.1, -12.6, 27.4]}