Question

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

x= -2, 0, 4
f(x)= 2.5, 1.5, -60.5

Answer 1

y=-2.5
`x^(2)`+4.5x+1.5

Explanation:

standard form of equation of parabola is,

y=a
`x^(2)`+bx+c

For x=0

1.5=0a+0b+c

1.5=c

For x=-2,

2.5=4a-2b+c

substituting the value of c

2.5=4a-2b+1.5

on solving,

4a-2b=1____________(1)

For x=4,

-60.5=16a+4b+c

substituting the value of c,

-60.5=16a+4b+1.5

on solving,

16a+4b=-62_______(2)

Multiplying equation 1 by 2,

8a-4b=2_______(3)

adding equation 2 and 3

16a+4b+8a-4b=-62+2

24a=-60

on solving,

a=-2.5

substituting the value of a in equation 1,

10-2b=1

2b=9

b=4.5

hence, equation of parabola in standard form is,

y=-2.5
`x^(2)`+4.5x+1.5