Lesson 2 Transformers: More Than Meets the y’s Solidify Understanding

Ready

The standard form of a quadratic equation is defined as $y = a x^{2} + b x + c, (a \neq 0)$ .

Identify $a$ , $b$ , and $c$ in the following equations.

Example: Given $4 x^{2} + 7 x - 6,$ $a = 4$ , $b = 7$ , and $c = - 6$

1.

$y = 5 x^{2} + 3 x + 6$

$a =$

$b =$

$c =$

2.

$y = x^{2} - 7 x + 3$

$a =$

$b =$

$c =$

3.

$y = - 2 x^{2} + 3 x$

$a =$

$b =$

$c =$

4.

$y = 6 x^{2} - 5$

$a =$

$b =$

$c =$

5.

$y = - 3 x^{2} + 4 x$

$a =$

$b =$

$c =$

6.

$y = 8 x^{2} - 5 x - 2$

$a =$

$b =$

$c =$

Multiply and write each product in the form $y = a x^{2} + b x + c$ . Then identify $a$ , $b$ , and $c$ .

7.

$y = x (x - 4)$

Equation:

$a =$

$b =$

$c =$

8.

$y = - 7 x (2 x - 1)$

Equation:

$a =$

$b =$

$c =$

9.

$y = 11 (3 x^{2} + 5)$

Equation:

$a =$

$b =$

$c =$

10.

$y = 17 (- 2 x^{2} + 3 x)$

Equation:

$a =$

$b =$

$c =$

11.

$y = x (x - 6) + 4 (- x + 1)$

Equation:

$a =$

$b =$

$c =$

12.

$y = x (x - 8) + 2 (4 x + 15)$

Equation:

$a =$

$b =$

$c =$

Set

Graph the following equations. State the vertex. (Be precise and graph at least five points.)

13.

$y = {(x - 1)}^{2}$

Vertex:

14.

$y = {(x - 1)}^{2} + 1$

Vertex:

15.

$y = 2 {(x - 1)}^{2} + 1$

Vertex:

16.

$y = {(x + 3)}^{2}$

Vertex:

17.

$y = - {(x + 3)}^{2} - 4$

Vertex:

18.

$y = - 0.5 {(x + 1)}^{2} + 4$

Vertex:

19.

Explain which values for $a$ and $c$ (given that $a \neq 0$ ) in the equation $f (x) = a x^{2} + c$ would produce a graph that fits each description.

a.

A parabola with two $x$ -intercepts.

b.

A parabola with no $x$ -intercepts.

Go

Use the table to identify the vertex, the equation for the line of symmetry, and state the number of $x$ -intercept(s) the parabola will have, if any. State whether the vertex will be a minimum or a maximum.

20.

$x$	$y$
$- 4$	$10$
$- 3$	$3$
$- 2$	$- 2$
$- 1$	$- 5$
$0$	$- 6$
$1$	$- 5$
$2$	$- 2$

a.

Vertex:

b.

Line of symmetry:

c.

$x$ -intercept(s):

d.

Minimum or Maximum?

21.

$x$	$y$
$- 2$	$49$
$- 1$	$28$
$0$	$13$
$1$	$4$
$2$	$1$
$3$	$4$
$4$	$13$

a.

Vertex:

b.

Line of symmetry:

c.

$x$ -intercept(s):

d.

Minimum or Maximum?

22.

$x$	$y$
$- 7$	$- 9$
$- 6$	$3$
$- 5$	$7$
$- 4$	$3$
$- 3$	$- 9$
$- 2$	$- 29$
$- 1$	$- 57$

a.

Vertex:

b.

Line of symmetry:

c.

$x$ -intercept(s):

d.

Minimum or Maximum?

23.

$x$	$y$
$- 8$	$- 9$
$- 7$	$- 8$
$- 6$	$- 9$
$- 5$	$- 12$
$- 4$	$- 17$
$- 3$	$- 24$
$- 2$	$- 33$

a.

Vertex:

b.

Line of symmetry:

c.

$x$ -intercept(s):

d.

Minimum or Maximum?