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Square root
Zeros
Basics
Word problems
Bonus
100

Solve for x:

x2-4=0

x=± 2

100

What are the zeros based on the table?

x  |  y

-4     6

-3     2

-2     0

-1     -2

0      -3

1      0

The zeros are:

x=-2

x=1

REMEMBER: y must equal 0 for x-intercepts

100

What's the vertex of the following:

y=3(x-6)2-4

(6,-4)

100

Timmy throws a baseball and it creates a path described by the equation:

h=-2t2+8t+7

What's the MAXIMUM height?

Maximum is at the vertex:

t=-(8)/2(-2) = -8/-4 = 2

h=15

100

Classify each term as constant, linear, or quadratic:

25x2-7x+8

25x2:quadratic

-7x:Linear

8:Constant

200

Solve for x:

x2+36=0

x=±6i

200

What are the zeros based on the table?

x  |  y

-4     5

-3     4

-2     3

-1     1

0      0

1      -1

2      0

The zeros are:

x=0

x=2

200

What are the x-intercepts of: 

y=2x2-5x-3

(-1/2,0)

(3,0)

200

Timmy throws a baseball and it creates a path described by the equation:

h=-3t2+12t+7

What's the MAXIMUM height?

t=-12/-6=2

h=19

200

What is the y-intercept of:

y=-x2-265x+9

(0,9)

300
Solve for x:

2x2 + 4 = 12

x=± 2

300

When Aaron solved the equation, y=x2+6x+5, he found the solutions x=-1 and x=-5. How are those solutions related to the x-intercepts?

The solutions are the same as the x-intercepts. That's where the name "zeros" comes from. 

300

What are the roots of:

y=x2-2x-8

x=-2

x=4

300

The length of a rectangle is 3 less than its width. What is the lowest reasonable width possible?

Length = Width - 3

If width is 0, length would be negative, that's impossible.

The lowest reasonable width is 3.

3<w<infinity

300

What are the x-intercepts of:

y=x2+8x+7

(-7,0)

(-1,0)

400

Solve for x:

(x-3)2=25

x=-2

x=8

400

Solve for x:

x2+14=9x

x=2,x=7

400

What is the axis of symmetry of:

y=-x2+2x-5

What is the vertex?

Axis of Symmetry:

x=1

Vertex:

(1,-4)

400

A garden area is 5 ft by 5 ft. The garden is enclosed by an even length of sidewalk all around. The area of the sidewalk AND the garden is 81 ft2. What is the width of the sidewalk?

Total area = Length x Width


81 = (5+2x)(5+2x)

x = 2

400

On the graph of a quadratic function, the x-intercepts are (0,0) and (−16,0), and the vertex is (−8,4). Which equation represents the function?

A. y= 16(x+8)2+4

B. y=1/16 (x+8)2+4

C. y= -1/4 (x+8)2+4

D. y=-1/16(x+8)2+4

Substitute points to check which equation works.

D. y=-1/16(x+8)2+4

500

Solve for x:

(x+4)2=16

x=0

x=-8

500

If the x-intercepts of a parabola are (-2,0) and (7,0), what could the quadratic equation in standard form be?

y=(x+2)(x-7)

y=x2-5x-14

500

What is the y-intercept of the following:

y=-x2+507x-3

(0,-3)

500

A garden area is 6 ft by 5 ft. The garden is enclosed by an even length of sidewalk all around. The area of the sidewalk AND the garden is 56 ft2. What is the width of the sidewalk?

Width = 1 ft

500

DOUBLE POINTS:

y = x2+x-6

Find the:

axis of symmetry

y-intercept

x-intercepts

vertex

axis of symmetry: x=-1/2

y-intercept: (0,-6)

x-intercepts: (-3,0) (2,0)

vertex: (-1/2, -25/4)