Topic 4: Quadratics

Solving by Factoring

100

Solve (x – 3)(x + 4) = 0 by factoring.

x =3 and -4

200

Solve x² + 5x + 6 = 0

x = -3 and -2

300

Solve x² – 3 = 2x

x = -1 and 3

400

Solve (x + 2)(x + 3) = 12

x = -6 and 1

500

Solve:

1) x² + 5x = 0

2) x² – 4 = 0

1) x = 0 and -5

2) x = -2 and 2

Completing the Square

100

Completing the square is where we...

Transform ax²+bx+c = 0 into a(x+d)² + e = 0 and solve for x

200

Solve x² + 6x – 7 = 0 by completing the square.

x = -7 and 1

300

Solve x² + 4x + 1 = 0

x = +/-√3 - 2

400

Solve 5x² – 4x – 2 = 0

x = +/-√0.56 +.04

500

Solve x² + 10 = –6x

x = -3 +/-i

Quadratic Formula

100

What is the Quadratic Formula?

x=(-b +/-√(b²-4ac))/2a where ax²+bx+c

200

What is the discriminant and what does it do?

The part of the quadratic formula that looks like (b²-4ac) that determines how many solutions there are to the given quadratic equation.

+ discriminant = two distinct real number solutions

discriminant of 0 = a repeated real number solution

- discriminant = zero real number solutions

300

How many solutions does 6x² + 10x − 1 = 0 have?

Two

400

What are the solutions to x² - 10x + 20 = 0

x = 5 +/-√5

500

What are the solutions to 2x² - 2x - 5 = 0

(1 +/-√11)/2

Solving by Taking Roots

100

Solve x² - 4 = 0 by taking the square root.

x = +/-2

200

Solve 2x² + 3 = 131 by taking the square root.

x = +/-8

300

Solve 9x² + 56 = 47 by taking the square root.

x = +/-i

400

Solve x² - 50 = 0 by taking the square root.

x = +/-5√2

500

Solve ___ by taking the square root.

1) (x - 5)² - 100 = 0

2) (x - 2)² - 12 = 0

!) x = -5 and 15

2) 2 +/-2√3

Transformations of Graphs

100

Describe the shift that occurs between F(x) = x² and F(x) = x² - 5 on a graph.

Shift down of 5 units

200

Describe the shift that occurs between F(x) = x² and F(x) = (x - 5)² on a graph.

Shift of 5 units right

300

Describe the shift that occurs between F(x) = x² and F(x) = _x² on a graph.

1) 2

2) 0.5

1) Stretches the graph vertically by a factor of 2

2) Compresses the graph vertically by a factor of 2

400

Describe the shift that occurs between F(x) = x² and F(x) = -x² on a graph.

It flips the parabola upside-down

500

Describe the shifts that occurs between F(x) = x² and F(x) = -(1/3)(x+9)²+6 on a graph.

The parabola flips upside-down, is vertically compressed by a factor of 3, and is shifted 9 units left and 6 units up.