Question

What is the equation, in standard form, of a parabola that contains the following points (–2, 18), (0, 4), (4, 42)?

Answer 1

`y=11/4x^2-3/2x+4`

Explanation:

The standard form of a quadratic equation is

`y=ax^2+bx+c`.

Here, when `x=0`, `y=4`, so it is easy to determine `c`.

`4=a*0^2+b*0+c=c`

`c=4`

We have two more points with which to create two equations and two unknowns, `a`, and `b`.

`18=a(-2)^2+b(-2)+4=4a-2b+4`

`42=a(4)^2+b(4)+4=16a+4b+4`

We can subtract 4 from both sides of these equations and divide the second equation by 2.

`4a-2b=14`

`8a+2b=19`

Now add the two equations together.

`12a=33`

`a=11/4`

Substitute this value of `a` into either equation to get

`b=-3/2`

This makes our final equation

`y=11/4x^2-3/2x+4`