Activity A.1.5.
(a)
Make a plot of the parabola given by \(x=y^2\text{.}\) You should draw and label the vertex and four other points on the parabola.
(b)
Draw a plot of the graph for \(2x=y^2\) and label the vertex and four other points. What transformation is done to change the graph of the parabola given by \(x=y^2\) to the graph of \(2x=y^2\text{?}\) Be specific about how the graph of \(2x=y^2\) is different than the graph of \(x=y^2\text{.}\)
(c)
Draw a plot of the graph for \(y=x^2\) and label the vertex and four other points on the parabola. What transformation is done to change the graph of the parabola given by \(y=x^2\) to the graph of \(x=y^2\text{?}\) Be specific about how the graph of \(x=y^2\) is different than the graph of \(y=x^2\text{.}\)
(d)
What transformations are done to change the graph of \(x=y^2\) to the graph of \(\frac{x-1}{2}=\left(\frac{y+2}{3}\right)^2\text{?}\) Be specific about how the graph of \(\frac{x-1}{2}=\left(\frac{y+2}{3}\right)^2\) is different than the graph of \(x=y^2\) and specify if the transformations need to be done in a particular order.
(e)
Draw a plot of \(\frac{x-1}{2}=\left(\frac{y+2}{3}\right)^2\) and label the vertex and four other points on the parabola.
(f)
The graph of the equation \(x^2-8x-8y+8=0\) is an parabola. Convert this equation to the form \(\left(\frac{x-h}{a}\right)^2=\frac{y-k}{b}\) and use the idea of transformations from above to graph this parabola. Label the vertex and four other points on the parabola.
(g)
Give the equation of the parabola shown in Figure A.1.9
