Question

Write the standard form of the equation of a parabola passing through the point (1, 32) with a minimum point at (-2, 5).

Answer 1

`y=3x^2+12x+17`

Explanation:

The equation in vertex form is
`y=a(x+2)^2+5`.

We can use the point
`(1,32)` to solve for
`a`.

`32=a(1+2)^2+5 \\ \\ 27=9a \\ \\ a=3 \\ \\ \\ \therefore y=3(x+2)^2 + 5 \\ \\ =3(x^2+4x+4)+5 \\ \\ =3x^2+12x+12+5 \\ \\ =3x^2+12x+17`