Question

what is the equation, in standard form, of a parabola that contains the following points? ( -2, -23.5)(0,-4.5)(4,-26.5)

Answer 1

y = -2.5x^2 + 4.5^x + -4.5

Answer 2

The equation of parabola is
`y=-(5)/(2)x^2+(9)/(2)x-4.5`.

Explanation:

Equation of a parabola is quadratic equation.

Let the equation of parabola be

`y=Ax^2+Bx+C` .... (1)

The parabola contains points ( -2, -23.5), (0,-4.5), (4,-26.5).

Put (0,-4.5) in equation (1),

`-4.5=A(0)^2+B(0)+C`

`-4.5=C`

Put this value in equation (1).

`y=Ax^2+Bx-4.5` ... (2)

Put ( -2, -23.5) and (4,-26.5) in equation (2).

`-23.5=A(-2)^2+B(-2)-4.5`

`-19=4A-2B` .... (3)

`-26.5=A(4)^2+B(4)-4.5`

`-22=16A+4B` .... (4)

On solving (3) and (4), we get

`A=-(5)/(2)` and
`B=(9)/(2)`

Therefore the value of parabola is

`y=-(5)/(2)x^2+(9)/(2)x-4.5`