Question

Find a formula for a quadratic function with the zeros -4 and 1. One point on thegraph is (-3,-4).

Answer 1

The quadratic formula can be expressed as a function of its zeros:

`y(x)\text{ = a}\cdot(x-x_1)\cdot(x_{}-x_2)`

Where x1 and x2 are the zeros of the equation and "a" is a constant.

`\begin{gathered} y(x)\text{ = a}\cdot(x\text{ - (-4))}\cdot(x-1) \\ y(x)\text{ = a}\cdot(x+4)\cdot(x-1) \end{gathered}`

To find the constant we need to apply the point (-3,-4).

`\begin{gathered} -4\text{ = a}\cdot(-3+4)\cdot(-3-1) \\ -4\text{ = a}\cdot(1)\cdot(-4) \\ -4=-4a \\ a\text{ = }(-4)/(-4)\text{ = 1} \end{gathered}`

Therefore the quadratic expression:

`\begin{gathered} y(x)=(x+4)\cdot(x-1) \\ y(x)=x^2-x+4x-4 \\ y(x)=x^2+3x-4 \end{gathered}`