Question

A quadratic function, f (x), can be written in equivalent forms to reveal different information about the function. Move the options to the blanks to describe the property that is best revealed by each form.

Answer 1

A quadratic function, f (x), can be written in equivalent forms to reveal different information about the function.

The following quadratic equation is written in vertex form

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

This form is used to identify the vertex (h, k) of the quadratic equation.

The vertex is the maximum/minimum point of the quadratic equation.

So, for the 1st equation, vertex is the answer.

The following quadratic equation is written in the standard form

$f(x)=ax^2+bx+c$

This form is used to identify the y-intercept of the quadratic equation by substituting x = 0 into the equation.

The y-intercept is the point where the equation intersects the y-axis.

So, for the 2nd equation, y-intercept is the answer.

The following quadratic equation is written in the factored form.

$f(x)=(x-m)(x-n)$

The form is used to identify the x-intercepts of the quadratic equation by substituting f(x) = 0 into the equation.

The x-intercepts are the points where the equation intersect the x-axis.

x = m and x = n are the two x-intercepts (they are also known as roots of the equation or solutions of the equation)

So, for the 3rd equation, x-intercepts is the answer.