4.11 Graphing quadratic functions

Graph by plotting points. Make sure to include positive and negative values of $x$ !

$y=x^2$

Note that there is a little point at the bottom of the graph. This point is called the “vertex.”

Graph each of the following by drawing these as variations of #1—that is, by seeing how the various numbers transform the graph of $y=x^2$ . Next to each one, write down the coordinates of the vertex.

$y=x^2+3$

Vertex:

$y=x^2-3$

Vertex:

$y=(x-5{)}^2$

Vertex:

Plot a few points to verify that your graph of #4 is correct.

$y=(x+5{)}^2$

Vertex:

$y={\mathrm{2x}}^2$

Vertex:

$y=\frac{1}{2}{x}^2$

Vertex:

$y=-x^2$

Vertex:

$y=(x-5{)}^2-3$

Vertex:

Make a graph on the calculator to verify that your graph of #10 is correct.

$y=2(x-5{)}^2-3$

Vertex:

$y=-2(x-5{)}^2-3$

Vertex:

$y=\frac{1}{2}(x+5{)}^2+3$

Vertex:

Where is the vertex of the general graph $y=a(x-h{)}^2+k$ ?

Graph by plotting points. Make sure to include positive and negative values of $y$ ! $x=y^2$

$x=y^2+4$

$x=(y-2{)}^2$

Plot a few points to verify that your graph of #18 is correct.

$x=-y^2$

$x=-2(y-2{)}^2+4$