Question

What attribute(s) of the graph of a parabola can you immediately find given the factored form of a quadratic function? What attribute(s) of the graph of a parabola can you immediately find given the vertex form of a quadratic function?

Answer 1

The factored form of a quadratic equation is

`y=a(x-m)(x-n)`

Where
`m` and
`n` are real numbers.

Though this form, we can deduct the parabola direction, if it opens upside or downside. Additionally, we can also deduct the x-axis interceptions, which in this case are
`x=m` and
`x=n`, they are also called the roots of the equation.

The vertex form of a quadratic equation is

`y=a(x-h)^(2) +k`

Using this form we can deduct the parabola direction, if opens up or down. Also, we can deduct the vertex of the parabola, which has coordinates
`(h,k)`, parameters of the vertex form.

Therefore, as you can observe, the different forms of a quadratic equation can give us different information.