The Quadratic Quest!

Factoring

100

                      Factor: 4x² + 12x + 9

Answer: (2x+3)²

200

What are the solutions for the equation:

                               x²-7x=18

Answer: -2 and 9

300

What are the factors of 5x²-30x-80?

Answer: (x-8)(x+2)

400

       What are the factors of the equation below?

                            x² - x - 42 = 0

Answer: -6 and 7

500

                       Factor this expression. 

                                2x²-18

Answer: 2(x²-9)

Graphing

100

What is the y-intercept of the quadratic equation:

                           - x² + 6x - 8

Answer : (0,-8)

200

Find the y-intercept of the equation below : 

                         x² + 5x + 6

Answer : (0,6)

300

Find the vertex of the following equation :

                          y = -x² + 6x - 8

Answer : ( 3 , 1 )

400

find the axis of symmetry of the following equation : 

                     x² - x - 6

answer : 0.5 or 1/2

500

what are the x-intercepts of the equation below : 

             x² - 2x - 3

answer : x = 3 and x = -1

Multiple Choice

100

find the solutions to x² + 13x = 40.

A) x = -8 and x = -5

B) x = -40 and x = -1

C) x = 5 and x = 8

D) x = 98 and x = -5

answer : A) x = -8 and x = -5

200

What is the maximum of the equation: -x² + 8x + 6

A. 4

B. -22

C. -4

D. 22

Answer: D. 22

300

What equation is equivalent to the problem: 6x²+3x-9?

A. -3(2x-3)(x-1)

B. 3(2x+3)(x-1)

C. 3(2x-3)(x+1)

Answer: B. 3(2x+3)(x-1)

400

Which equation best matches the graph shown below?

- 4 units to the right

- 1 unit up

- narrower

- It has a maximum

_____________________________________

A. y = 2( x - 4 )² + 1                                   B. y = 2( x + 4)² + 1                                   C. y = -2( x + 4)² + 1                                 D. y = -2( x - 4)² + 1

Answer : D. y = -2( x - 4)² + 1

500

which of the following is the Y-INTERCEPT of the Equation x² - 9x.

A. (0,9/2)

B. (0,0)

C. (9,0)

D. (1,-8)

E. (8,-8)

Answer : B. (0,0)

True or False

100

T or F: The line that crosses in the middle of the quadratic graph is the axis of symmetry.

Answer: True

200

True or false? The equation for Axis of Symmetry is 

                      y = ##

Answer : False

300

True or False : Every Quadratic function has exactly 2 solutions.

Answer : False

*Quadratic functions can have 0, 1, or 2 solutions*

400

True or False : Jason was given the quadratic equation: -x²+10x-24 He says that the two solutions for this problem are 5 and 6.

Answer: False

500

True or False : If the leading coefficient a is negative, the parabola is downward and has a maximum.

Answer : True

Quadratics Vocab

100

What are all the names for when the lines cross over the x-axis in quadratic equations? (Must name them all)

Answer: x-intercepts, zeros, solutions, and roots.

200

What is the y-intercept?

Answer: When the line/point crosses the y-axis.

300

What is another name for the quadratic graph?

Answer : Parabola

400

What is the Vertex of a graph?

Answer : the highest or lowest point on a parabola

500

What is the vertical line passing through the vertex?

Answer : Axis of Symmetry