What is the equation, in standard form, of a parabola that models the values in the table? x -1 0 2 f(x) 12 5 15 a. y= -4x^2+3x+5 b. y= -4x^2-3x+5 c. y= 3x^2-4x+5 d. y= 4x^2-3x+5

The correct option is D.

Step-by-step explanation:

The standard form of a parabola is

           .... (1)

From the table it is clear that the parabola passing through the points (-1,12), (0,5) and (2,15).

Substitute x=0 and y=5 in equation (1).

Substitute c=5, x=-1 and y=12 in equation (1).

                ... (2)

Substitute c=5, x=2 and y=15 in equation (1).

                ... (3)

On solving (2) and (3), we get

Substitute a=4,b=-3 and c=5 in equation (1).

The standard form of the parabola is . Therefore the correct option is D.

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:

for (-1,12)

This does not give 12 as the answer and is not a solution.

for (-1,12)

This does not give 12 as the answer and is not a solution.

for (-1,12)

This does give 12 as the answer and is a possible solution.

We now try (2,15).

This does not give 15 as the answer and is not a possible solution.

for (-1,12)

This does not give 12 as the answer and is not a solution.

We now try (2,15).

This does give 15 as the answer and is a solution.

This is the standard form of the equation.