Answer:
[tex]Y=4x^2+3x-6[/tex]
Step-by-step 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:
[tex]Y=3x^2+4x-6[/tex] for (-2,4)
[tex]Y=3(-2)^2+4(-2)-6=3(4)+-8-6=12+-8-6=-2\\[/tex]
This does not give 4 as the answer and is not a solution.
[tex]Y=4x^2+3x-6[/tex] for (-2,4)
[tex]Y=4(-2)^2+3(-2)-6=4(4)+-6-6=16+-6-6=-4\\[/tex]
This does give 4 as the answer and is a possible solution.
[tex]Y=4x^2-3x-6[/tex] for (-2,4)
[tex]Y=4(-2)^2-3(-2)-6=4(4)+6-6=16+6-6=16\\[/tex]
This does not give 4 as the answer and is not a solution.
[tex]Y=-4x^2-3x-6[/tex] for (-2,4)
[tex]Y=-4(-2)^2-3(-2)-6=-4(4)+6-6=-16+6-6=-16\\[/tex]
This does not give 4 as the answer and is not a solution.
The only possible solution is [tex]Y=4x^2+3x-6[/tex]
