Algebra Unit 6: Quadratics

Identifying Key Features

100

What are the roots of the equation

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

x=-5 and x=2

200

What is the y-intercept of the equation

y=7x^2-47x+8

8

300

What is the vertex of the following equation. You can solve this using any method.

y=-x^2+2x+3

(1,4)

400

What is the axis of symmetry of the following equation. You MUST solve this algebraically.

y=2x^2-6x+3

3/2 or 1.5

500

What is the axis of symmetry AND vertex of the following equation. You MUST solve this algebraically.

y=x^2-8x+10

Axis of Symmetry: x=4

Vertex: (4,-6)

Finding Roots

100

Find the roots of the following equation algebraically

y=x^2+8x+15

-3 and -5

200

Find the roots of the following equation algebraically

y=x^2+4x-32

-8 and 4

300

Find the roots of the following equation algebraically

y=x^3-6x^2-27x

9 and 3

400

Find the roots of the following equation algebraically

y=2x^2-10x+12

2 and 3

500

Find the roots of the following equation algebraically

2x^3-10x^2+8x

0, 1, and 4

Solving using Square Roots

100

Solve for the roots.

x^2=25

+5 and -5

200

Solve for the roots.

x^2-49=0

+7 and -7

300

Solve for the roots.

x^2+16=0

No real solutions

400

Solve for the roots.

9x^2=36

-2 and 2

500

Solve for the roots.

2x^3-200x=0

-10, 0, and 10

Quadratic Formula

100

Solve using the quadratic formula

x^2-5x-14=0

7 and -2

200

Solve using the quadratic formula

2x^2+2x-12=0

2 and -3

300

Solve using the quadratic formula

x^2-4x+4=0

2

400

Solve using the quadratic formula

2x^2+3x-20=0

5/2 and -4

500

Solve using the quadratic formula

2x^ 2 − 7x − 13 = −10

(7+-\sqrt73)/4

Transformations

100

Describe the transformation of the parent function, given the following equation: 

y = (x - 4)^2 +1

Shift right 4 units; up 1 unit

200

Describe the transformation of the parent function, given the following equation: 

y = x^2 - 6

Shift 6 units down

300

Describe the transformation of the parent function, given the following equation: 

y = (x + 7)^2

Shift 7 units left

400

Describe the transformation of the parent function, given the following equation: 

f(x) = 2(x - 40)^2 - 2

Narrower by 2 units; Shift 40 units right; Shift 2 units down

500

Describe the transformation of the parent function, given the following equation: 

f(x) = -3(x + 2)^2 -1

Reflect over the x-axis; Narrower by 3 units; Shift 2 units left; Shift 1 unit down