Chapter 7.5, Problem 39WE

(a)

To determine

Find a general equation that represents all parabolas that have horizontal axis.

Answer to Problem 39WE

  $x-h=a{(y-k)}^2$

Explanation of Solution

Calculation:

Comparing to the equation of all parabolas that have vertical axis , $y-h=a{(x-k)}^2$ , we can form an equation that represents all parabolas that have horizontal axis ( just the x and y -intercepts are reversed):

  $x-h=a{(y-k)}^2$

(b)

To determine

Find the number of x- intercepts and y -intercepts that a parabola with horizontal axis of symmetry have.

Answer to Problem 39WE

A parabola with horizontal axis of symmetry can have atmost1 x- intercept and atmost 2 y -intercepts.

Explanation of Solution

Calculation:

It goes analogues to the parabola with vertical axis of symmetry , just the x- intercepts and y -intercepts are interchanged.

So, a parabola with horizontal axis of symmetry can have only 1 x -intercept, since in its equation , substitute y =0:

  $x-h=a{(0-k)}^2$ , we get only 1 x -value.

It can have 0, 1 , or 2 y -intercepts , since in its equation , substitute x = 0 :

  $\begin{array}{l}0-h=a{(}^y\\ \Rightarrow y=k\pm \sqrt{\left(-\frac{h}{a}\right)}\end{array}$

So, a parabola with horizontal axis of symmetry can have atmost1 x- intercept and atmost 2 y -intercepts.