Question Type 1: Drawing the effect of single transformations on a graph Exercises

Sketch $y = \left(\frac{x}{3}\right)^2 - 2$ using $y = x^2 - 2$.

On the same axes as $y=x^2-2$, sketch $y=\frac{1}{2}(x^2-2)$. Mark the images of $(2,2)$ and $(-2,2)$.

Draw the graph of $y = (x+2)^2 - 2$ from $y = x^2 - 2$.

Sketch the graph of $y = (x-3)^2 - 2$ by transforming the graph of $y = x^2 - 2$.

Sketch the graph of $y = (2x)^2 - 2$ from $y = x^2 - 2$.

Sketch the graph of $y = 4(x^2 - 2)$ given the graph of $y = x^2 - 2$. Label the images of the points $(0,-2)$, $(1,-1)$, and $(-1,-1)$.

Sketch $y = x^2 + 3$ given $y = x^2 - 2$.

On a coordinate grid, sketch $y=x^2-5$ from $y=x^2-2$.

Sketch $y=4x^2-2$ and identify the transformation from $y=x^2-2$.

Sketch the graph of $y = |x^2 - 2|$.