Question

What is the equation, in standard form, of a parabola that models the values in the table?

Answer 1

`Y=4x^2+3x-6`

Explanation:

For the standard form equation to model the values in the table, each value of x in the table should give the matching the y value when substituted into the equation. We will test each equation:

`Y=3x^2+4x-6` for (-2,4)

`Y=3(-2)^2+4(-2)-6=3(4)+-8-6=12+-8-6=-2\\`

This does not give 4 as the answer and is not a solution.

`Y=4x^2+3x-6` for (-2,4)

`Y=4(-2)^2+3(-2)-6=4(4)+-6-6=16+-6-6=-4\\`

This does give 4 as the answer and is a possible solution.

`Y=4x^2-3x-6` for (-2,4)

`Y=4(-2)^2-3(-2)-6=4(4)+6-6=16+6-6=16\\`

This does not give 4 as the answer and is not a solution.

`Y=-4x^2-3x-6` for (-2,4)

`Y=-4(-2)^2-3(-2)-6=-4(4)+6-6=-16+6-6=-16\\`

This does not give 4 as the answer and is not a solution.

The only possible solution is
`Y=4x^2+3x-6`