Practice section 4 of 9

Describe how the graph of $y=5x^2-20x+16$ is obtained from $y=x^2$ using a sequence of transformations.

The curve $y=x^3$ is transformed by a translation of 2 units in the positive x-direction, followed by a stretch with scale factor $1/2$ parallel to the y-axis, followed by a translation of 6 units in the negative y-direction. Find the equation of the new curve in the form $y=f(x)$ and the exact coordinates of the points where this curve crosses the x- and y-axes. Sketch the new curve.

A graph $y=f(x)$ undergoes three successive transformations: A, a scaling parallel to the x-axis with scale factor $1/2$; B, a translation of 3 units in the positive x-direction; C, a reflection in the x-axis. The resulting equation is $y=-\ln(6-2x)$. Determine the equation of the graph $y=f(x)$, showing your working clearly.

Under two successive transformations, $y=x$ becomes $y=3x-2$. Describe the transformations.

Use a graphing calculator to sketch (1) $y=x^2-1$ and (2) $y=|x^2-1|$. Copy the curves. What do you observe about the curves?

Sketch $y=|(x+1)(x-2)(x-3)|$ from $y=(x+1)(x-2)(x-3)$.