Question

Name the three forms of quadratic functions and for each form, list all features we can use to characterize the equation.

Answer 1

The three forms of quadratic functions are: standard form, factored form, and vertex form.

Standard form

$y=ax^2+bx+c$

The value of coefficient c indicates the y-intercept of the function

Factored form

$y=a(x-x_1)(x-x_2)$

x₁ and x₂ are the x-intercepts (or zeros or roots) of the function

Vertex form

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

The point (h, k) is the vertex of the function.

In the three cases, the value of coefficient a indicates the end behavior of the function. If a > 0, then the curve opens up, if a < 0, then the curve opens down.