Graphing Quadratic Functions

Vocabulary

100

What is the name used to describe a U-shaped graph for a quadratic function?

Parabola

200

Where are the solutions/zeroes of a quadratic located on a coordinate grid?

The x-axis

300

What do we call the highest or lowest point on a parabola (the center of the parabola).

Vertex

400

What do we call the line that runs through the vertex and cuts the parabola in half.

Axis of symmetry

500

When the parabola looks like a "U" pointing up to the sky, we say it is ________ _____

Concave Up

Factoring

100

Factor the binomial:

2x² + 10x

2x(x + 5)

200

Factor the binomial:

49x² - 81

(7x + 9)(7x - 9)

300

Factor the quadratic:

3x² - 15x + 18

3(x - 2)(x - 3)

400

Factor the quadratic:

3x² + 4x - 4

(x + 2)(3x - 2)

500

Factor the quadratic:

10x² - 15x - 45

5(x - 3)(2x + 3)

Solving by Square Roots

100

Solve for x.

x² - 16 = 33

x = 7

x = -7

200

Solve for x.

(x - 2)² - 8 = 1

x = 5

x = -1

300

Solve for x.

6x² - 10 = 62

x = 2√3

x = -2√3 

400

-3(x + 5)² + 2 = -145

x = 2

x = -12

500

Solve for x.

1/2 (x - 1)² + 4 = 12

x = 5

x = -3

Axis of Symmetry & Vertex

100

Find the vertex:

f(x) = 2(x + 3)² - 4

(-3, -4)

200

Find the vertex:

f(x) = -4(x - 8)² + 5

(8, 5)

300

Find the vertex:

f(x) = x² + 4x + 4

(-2, 0)

400

Find the vertex:

f(x) = 2x² -8x +13

(2, 5)

500

Find the vertex:

f(x) = 4x² -4x +7

(1/2, 6)

Finding Zeros

100

Find the zeroes:

y=(x-2)(x+6)

x = 2

x = -6

200

Find the zeroes:

m² - m = 0

m = 0

m = 1

300

Find the zeroes:

m² + 3m - 40 =0

m = 5

m = -8

400

Find the zeroes:

3a² - 14a + 18 = 3

a = 3

a = 5/3

500

Find the zeroes:

2(x² - 2) + x = 4x -5

x= 1

x = 1/2