Answer:
Y=4x^2-3x+5
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=-4x^2+3x+5[/tex] for (-1,12)
[tex]Y=-4(-1)^2+3(-1)+5=-4(1)+-3+5=-4+-3+5=-2\\[/tex]
This does not give 12 as the answer and is not a solution.
[tex]Y=-4x^2-3x+5[/tex] for (-1,12)
[tex]Y=-4(-1)^2-3(-1)+5=-4(1)+3+5=-4+3+5=4\\[/tex]
This does not give 12 as the answer and is not a solution.
[tex]Y=3x^2-4x+5[/tex] for (-1,12)
[tex]Y=3(-1)^2-4(-1)+5=3(1)+4+5=3+4+5=12\\[/tex]
This does give 12 as the answer and is a possible solution.
We now try (2,15).
[tex]Y=3(2)^2-4(2)+5=3(4)-8+5=12-8+5=9\\[/tex]
This does not give 15 as the answer and is not a possible solution.
[tex]Y=4x^2-3x+5[/tex] for (-1,12)
[tex]Y=4(-1)^2-3(-1)+5=4(1)+3+5=4+3+5=12\\[/tex]
This does not give 12 as the answer and is not a solution.
We now try (2,15).
[tex]Y=4(2)^2-3(2)+5=4(4)-6+5=16-6+5=15\\[/tex]
This does give 15 as the answer and is a solution.
This is the standard form of the equation.
