Quadratic Equations Review

Factoring

100

Use the Zero Product Property to solve the following quadratic equation. (x - 7)(x + 2) = 0

x = 7 or x = -2 

200

Solve the following quadratic equation by factoring. x²+3x+2 = 0

x = -2 or x = -1

300

Solve the following quadratic equation by factoring. x² - 6x + 5 = 0

x = 5 or x = 1

400

Solve the following quadratic equation by factoring. x² - 6x - 27 = 0

x = 9 or x = -3

500

Solve the following quadratic equation by factoring. 2x² - 5x - 3 = 0

x = -1/2 or x = 3

Square Roots

100

Solve the following quadratic equation by using square roots: x² = 4

x = 2 or x = -2

200

Solve the following quadratic equation by using square roots: x² = 121

x=11 or x=-11

300

Solve the following quadratic equation by using square roots: 4x² = 400

x = 10 or x = -10

400

Solve the following quadratic equation by using square roots: x² -9 = -8

x=1 or x=-1

500

Solve the following quadratic equation by using square roots: 5x² + 3 = 128

x=5 or x=-5

Rearrange and solve

100

Solve the following quadratic equation: x² + 6x = -8

x = -2 or x = -4

200

Solve the following quadratic equation: x² - 6x = -5

x = 1 or x = 5

300

Solve the following quadratic equation: x² - 24 = 2x

x = -4 or x = 6

400

Solve the following quadratic equation: x² = -10x -16

x = -2 or x = -8

500

Solve the following quadratic equation: 2x² - 8x = 10

x=5 or x=-1

Discriminant

100

What is the use of the discriminant in solving quadratics? 

The discriminant tells us whether there are two solutions, one solution, or no solutions of the equation.

200

a. Find the discriminant of x² + 6x + 5 = 0. 

b. State the number of solutions that the equation has. 

Formula: Δ=b² - 4ac

a. Δ=16 

b. Since Δ>0 (discriminant is positive), the equation has two distinct solutions.  

300

a. Find the discriminant of x² - 9x + 20 = 0. 

b. State the number of solutions that the equation has. 

Formula: Δ=b² - 4ac

a. Δ=1

b. Since Δ>0 (discriminant is positive), the equation has two distinct solutions. 

400

a. Find the discriminant of 2x² + 3x + 4 = 0. 

b. State the number of solutions that the equation has. 

Formula: Δ=b² - 4ac

a. Δ=-23

b. Since Δ<0 (discriminant is negative), the equation has no (real) solutions.

500

a. Find the discriminant of x² - 10x - 25 = 0. 

b. State the number of solutions that the equation has. 

Formula: Δ=b² - 4ac 

a. Δ=0

b. Since Δ=0, the equation has only one solution. 

Vertex

100

Find the vertex of f(x)=-x²+8x-15

(4,1)

200

Find the vertex of f(x)=x²-2x

(1,-1)

300

Find the vertex of f(x)=5x²+2x-2

(-1/5,-11/5)

400

f(x)=-x²-4x

(-2,4)

500

Find the vertex of x=5y²+4y+3

(11/5,-2/5)