Question

1. Write a quadratic function, in standard form, that fits the set of points. Solve it as a system of three equations

(-4, 9), (0, -7), and (1, -1)

Answer 1

The equation is
`y=2x^2+4x-7`

Explanation:

Let the quadratic function be

`y=ax^2+bx+c`

The point (-4,9) must satisfy this function,

`\Rightarrow a(-4)^2+b(-4)+c=9`

`\Rightarrow 16a-4b+c=9...(1)`

The point (0,-7) must also satisfy this function,

`\Rightarrow a(0)^2+b(0)+c=-7`

`\Rightarrow c=-7...(2)`

The point (1,-1) must also satisfy this function,

`\Rightarrow a(1)^2+b(1)+c=-1`

`\Rightarrow a+b+c=-1...(3)`

We put equation 2 into equation 1 to get;

`\Rightarrow 16a-4b-7=9`

`\Rightarrow 16a-4b=16`

`\Rightarrow 4a-b=4...(5)`

We again put equation 2 into equation 3 to get;

`\Rightarrow a+b-7=-1`

`\Rightarrow a+b=6...(6)`

We add equation 5 and 6 to get;

`5a=10`

`\Rightarrow a=2`

We put
`a=2` into equation 6 to get;

`2+b=6`

`\Rightarrow b=6-2`

`\Rightarrow b=4`

The equation is therefore
`y=2x^2+4x-7`