Solving Quadratic Equations

Factoring to Calculate the Roots

Completing the Square to Calculate the Roots

Find The Vertex by Completing the Square

Key Features of Quadratics by using Desmos

100

Factor to calculate the roots to the following quadratic:

x² - 5x - 14 = 0

x = 7 x = -2

100

Calculate the roots to the quadratic by completing the square.

x² + 6x + 8 = 0

x = -2 x = -4

100

Calculate the vertex by completing the square.

x²- 8x + 15 = 0

(4,1)

100

What is the y-intercept for the quadratic function?

x² + 5x - 12 = y

y-intercept = -12

200

Factor to calculate the roots to the following quadratic:

x²+ 3x + 2 = 0

x = -2 x = -1

200

Calculate the roots to the quadratic by completing the square.

x² - 6x = -5

x = 1 x = 5

200

Calculate the vertex by completing the square.

y = x²- 2x

(1,-1)

200

What are the roots the quadratic function?

x² - 6x + 12 = 0

no roots

300

Factor to calculate the roots to the following quadratic:

x² - 6x + 5 = 0

x = 5 x = 1

300

Calculate the roots to the quadratic by completing the square.

x² - 2x - 24 = 0

x = -4 x = 6

300

Calculate the vertex of the quadratic by completing the square.

x² + 10x + 16 = 0

(-5, -9)

300

What is the vertex for the quadratic function?

x² - 5x - 14 = 0

(2.5, -20.25)

400

Factor to calculate the roots to the following quadratic:

x² - 6x - 27 = 0

x = 9 x = -3

400

Calculate the roots to the quadratic by completing the square.

x² + 10x +16 = 0

x = -2 x = -8

400

Calculate the vertex of the quadratic by completing the square.

x² + 2x - 6 = 0

(-1, -7)

400

What is the line of symmetry for the parabola?

2x² + 4x - 8 = 0

x = -1

500

Factor to calculate the roots to the following quadratic:

2x² - 5x - 3 = 0

x = -1/2 x = 3

500

Calculate the roots to the quadratic by completing the square.

2x² - 8x = 10

x = 5 x = -1

500

Calculate the vertex of the quadratic by completing the square.

x² - 4x = -18

(2, 14)

500

Calculate the y-intercept, vertex, roots, and line of symmetry for the quadratic.

x² + 2x - 6 = 0

y-intercept: -6

vertex: (-1, -7)

roots: -3.646 and 1.646

line of symmetry: x = -1