Question

What is the equation of the parabola that has a vertex at `(-12, 5)` and passes through point `(-3,-15)`?

Answer 1

equation: `y=-20/81(x+12)^2+5`

Explanation:

Recall that the general equation for a quadratic equation in vertex form is:

`y=a(x-h)^2+k`

where:
`y=`y-coordinate
`a=`vertical stretch/compression
`x=`x-coordinate
`h=`horizontal translation or x-coordinate of vertex
`k=`vertical translation or y-coordinate of vertex

To find the equation of the parabola, substitute your known values into the equation to solve for the unknown variable:

`y=a(x-h)^2+k`

`-15=a(-3-(-12))^2+5`

`-20=a(9)^2`

`-20=a(81)`

`a=-20/81`

`:.`, the equation of the parabola is `y=-20/81(x+12)^2+5`.