Solving Quadratics
Complex Numbers
Graphing / Key Features
Applications of Quadratics
Converting Between Forms
100

Solve using any method:
x2 - 9x = -18

(x-6)(x-3) = 0

x = 6 , 3

100

Perform the Indicated Operation:
(5+4i) + (2 - 3i)

3 + i

100

Find the axis of symmetry:
-(x+5)2 - 7

Axis of Symmetry:

x = -5

100

Mr. Orders loses a really close game of Super Smash Brothers, and he gets upset and throws his controller. The height of the controller (in feet) can be modeled by the equation: -4x2 + x +3.
What is the maximum height his controller reaches?
(Round to 2 Decimal Places)

The controller reaches a maximum height of 3.06 feet

100

Convert the following to intercept form:
y = x2+3x-40

y = (x+8)(x-5)

200

Solve Using Any Method:
6x2 - 72x = 0

6x(x-12) = 0
x = 0, 12

200

Perform the Indicated Operation:
(7 - 3i) - (-2 + i)

(7+2) + (-3i - i)
9 - 4i

200

Find the vertex of the following quadratic:
x2+8x+19

xvertex = -b / 2a = -8 / 2 = -4
f(-4) = (-4)2 + 8(-4) + 19 = 3

vertex: (-4 , 3)

200

After how many seconds does Mr. Orders' controller reach maximum height? (Round to 2 Decimal Places)

After 0.13 seconds, the controller reaches maximum height.

200

Convert the following to standard form:
(2x+3)(x-5) = y

y = 2x2 - 7x - 15

300

Solve Using Any Method:
7x2 = 3x2 + 64

x2 = 16
x = +/- 4

300

Perform the Indicated Operation:
4i(3-5i)

12i - 20i2
-20i2 = 20

20 + 12i

300

Find the vertex of the following quadratic:
2x2+8x-3

xvertex = -8 / 2(2) = -2
f(-2) = 2(-2)2 + 8(-2) - 3 = -11

vertex: (-2, -11)

300

After how many seconds is Mr. Orders' controller 1.65 feet above the ground?

After 0.72 seconds, the controller is 1.65 feet off the ground.

300

Convert the following to intercept form:
y = 3x2-22x+7

y = (3x-1)(x-7)

400

Solve using any method:
x2 + 5x = 12

x = (-5 +/- sqrt(25 - 4(1)(-12))) / 2

(-5 +/- sqrt(73)) / 2 

400

Perform the Indicated Operation:
(7-9i)2

(7-9i)(7-9i)
49 - 126i + 81i2

-32 - 126i

400

Find the y intercept:

(x-2)2 - 5

y intercept - x = 0
f(0) = (0-2)2 - 5 = - 1
(0,-1) or y = -1

400

If Mr. Orders failed to catch the controller on its way down, how long would it take to hit the ground?

1 second

400

Convert the following to vertex form:
y = x2-6x+16

y - 16 = x2-6x
c = (b / 2)2 = (-6 / 2)2 = 9
y - 7 = (x-3)2
y = (x-3)2+7

500

Solve using any method:
3(x-8)2 = -243

x = 8 +/- 9i

500

Perform the Indicated Operation:
(2-7i)(4+3i)

8 - 28i + 6i -21i2
29 - 22i

500

Find the quadratic function passing through the point (-3,-1) with a vertex at (-2,-5). Give the equation in vertex form:

-1 = a(-3+2)2 -5
4 = a

y = 4(x+2)2- 5

500

A square backyard has a width of (3x) feet, a length of (x + 5) feet, and an area of 612ft2. Find the length and width of the backyard

x = 12

width: 3(12) = 36 ft
length 12+5 = 17 ft

500

Convert the following to standard form:
y = 3(x+2)2 - 25

y = 3x2+12x-13

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