Lesson 1 Transformers: Shifty y’s Develop Understanding

Ready

Make a point on the vertex, and draw a dotted line for the line of symmetry. Label the coordinates of the vertex, and state whether it’s a maximum or a minimum. Write the equation for the line of symmetry.

1.

2.

3.

4.

5.

6.

7.

What connection exists between the coordinates of the vertex and the equation of the axis of symmetry?

8.

The line of symmetry of a parabola is not always located on an easy-to-read point or line. Consider the parabola shown, and explain how you could find the line of symmetry.

9.

How many $x$ -intercepts are possible for a parabola?

10.

Sketch a parabola that has no $x$ -intercepts, and explain what would cause a parabola to not have any $x$ -intercepts.

Set

For problems 11–14, the table of values and graph for the quadratic parent function, $f (x) = x^{2}$ , is provided. Compare the values in the table for $g (x)$ in each question to those for $f (x)$ . Identify what stays the same and what changes.

11.

$x$	$f (x)$
$- 3$	$9$
$- 2$	$4$
$- 1$	$1$
$0$	$0$
$1$	$1$
$2$	$4$
$3$	$9$

$x$	$g (x)$
$- 3$	$2$
$- 2$	$- 3$
$- 1$	$- 6$
$0$	$- 7$
$1$	$- 6$
$2$	$- 3$
$3$	$2$

a.

Write the equation of $g (x)$ .

b.

Graph $g (x)$ on the same grid as $f (x)$ .

c.

How is the graph of $g (x)$ different than the graph of $f (x)$ ?

12.

$x$	$f (x)$
$- 3$	$9$
$- 2$	$4$
$- 1$	$1$
$0$	$0$
$1$	$1$
$2$	$4$
$3$	$9$

$x$	$g (x)$
$- 3$	$11$
$- 2$	$6$
$- 1$	$3$
$0$	$2$
$1$	$3$
$2$	$6$
$3$	$11$

a.

Write the equation of $g (x)$ .

b.

Graph $g (x)$ on the same grid as $f (x)$ .

c.

How is the graph of $g (x)$ different than the graph of $f (x)$ ?

13.

$x$	$f (x)$
$- 3$	$9$
$- 2$	$4$
$- 1$	$1$
$0$	$0$
$1$	$1$
$2$	$4$
$3$	$9$

$x$	$g (x)$
$- 3$	$4$
$- 2$	$1$
$- 1$	$0$
$0$	$1$
$1$	$4$
$2$	$9$
$3$	$16$

a.

Write the equation of $g (x)$ .

b.

Graph $g (x)$ on the same grid as $f (x)$ .

c.

How is the graph of $g (x)$ different than the graph of $f (x)$ ?

14.

$x$	$f (x)$
$- 3$	$9$
$- 2$	$4$
$- 1$	$1$
$0$	$0$
$1$	$1$
$2$	$4$
$3$	$9$

$x$	$g (x)$
$- 3$	$36$
$- 2$	$25$
$- 1$	$16$
$0$	$9$
$1$	$4$
$2$	$1$
$3$	$0$

a.

Write the equation of $g (x)$ .

b.

Graph $g (x)$ on the same grid as $f (x)$ .

c.

How is the graph of $g (x)$ different than the graph of $f (x)$ ?

Go

Graph each of the linear equations.

15.

$y = - 2 x + 7$

16.

$y = 3 (x + 2) - 5$

17.

$3 x + 5 y = 30$

18.

$f (x) = - \frac{1}{2} (x + 9) + 8$

19.

$- 4 x + 6 y = 36$

20.

$f (x) = \frac{1}{4} (x - 2) - 3$

21.

Linear equations can be written in different forms. Describe how to quickly graph a linear equation based on the form in which it is written.

a.

slope-intercept form:

b.

point-slope form:

c.

standard form: