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