Question

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

X: -2 0 4
F(x): 4 -6 70

Answer 1

Equation of parabola is:
`y=4x^(2) +3x-6`

Explanation:

By plotting a rough graph with the values given we get an opening upward parabola.

Standard equation for a parabola opening upwards is given by:

`y=ax^(2)+bx+c`

We can solve for a,b,c by substituting the given values of x and y.

Putting x=0 and y=-6 in the above equation,we get:

c = -6

Putting x=-2 and y=4, we get:

`4a-2b=10` ---------1

Putting x=4 and y=70, we get:

`16a+4b=76` --------2

Solving equation 1 and 2, we get

a=4 and b=3

Hence
`y=4x^(2) +3x-6`