Chapter 4.1, Problem 42PPSE

Solution

To find: The vertex, axis of symmetry, and transformations from the parent function $f\left(x\right)=\left|x\right|$ and $f\left(x\right)=x^2$ .

The vertex $\left(h,k\right)$ is equal to $\left(0,4\right)$ , the axis of symmetry is equal to $x=0$ .

The parent function $y=\left|x\right|$ and $y=x^2$ is translated $4$ unit up, vertically compressed by factor $2$ .

Given information:

The given functions are $y=-2\left|x\right|+4;y=-2{\left(x\right)}^2+4$ .

Calculation:

The given function is $y=-2\left|x\right|+4$ .

Compare $y=-2\left|x\right|+4$ with the general form $y=a\left|x-h\right|+k$ :

  $a=-2,h=0,k=4$

The vertex $\left(h,k\right)$ is $\left(0,4\right)$ .

The axis of symmetry is $x=0$ .

The parent function $y=\left|x\right|$ is translated $4$ unit up, vertically compressed by factor $2$ .

The given function is $y=-2{\left(x\right)}^2+4$ .

Compare $y=-2{\left(x\right)}^2+4$ with the general form $y=a{\left(x-h\right)}^2+k$ :

  $a=-2,h=0,k=4$

The vertex $\left(h,k\right)$ is $\left(0,4\right)$ .

The axis of symmetry is $x=0$ .

The parent function $y=x^2$ is translated $4$ unit up, vertically compressed by factor $2$ .