Solving Quadratic Equations and Polynomials

Factoring

100

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

x = 7 x = -2

200

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

x = -2 x = -1

300

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

x = 5 x = 1

400

Solve the following quadratic equation by factoring. 2x² + 7x +6 = 0

x = -1.5    x = -2

500

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

x = -1/2 x = 3

Square Roots AND Finding Solutions of Quadratic Equation

100

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

x = 2 x = -2

200

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

+11 or -11

300

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

x = 10 x = -10

400

What is the product of the two solutions of the equation x² + 9x + 18 = 0?

18    Explanation: The two solutions are x=-3 and x=-6 and (-3)(-6) = 18

500

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

x = 5 x = -5

Polynomials

100

Multiply the following.   8xy(2x − 3yz)

16x²y - 24xzy²

200

Which of the following is the sum of the two polynomials? 

       5x² − 7x + 4

       6x² − 3x − 3

11x² - 10x + 1

300

Expand the following: (x² + 3)(x² - 4x + 8)

x⁴ - 4x³ + 11x² - 12x + 24

400

For all m and n, (4m + n)(m² − n) = ?

4m³ - 4mn + nm² - n²

500

The sum of −1x² + 2x + 24 and 3x² + 4x − 11 can be written in the form ax² + bx + c, where a, b, and c are constants. What is the value of a + b + c?

a+b+c= 21   a=2 b=6 c=13         2x² + 6x +13

Quadratic Formula and Solving a Quadratic Equation

100

What is the quadratic formula?

x = -b +- sqrt(b² - 4ac) /(2a)

200

Solve the following quadratic equation by using the quadratic formula: x² + 6x + 5 = 0

x = -1         (-1,0)

x = -5          (-5,0)

300

What is a solution to the equation  x² + 25x = 0?  *Add 50 points for both solutions

x=-25       (25,0)

x=0           (0,0)

400

Solve the following quadratic equation by using the quadratic formula: 2x² + 9x + 4 = 0

x = -1/2         (-1/2,0)

x = -4             (-4,0)

500

Solve the following quadratic equation by using the quadratic formula: 4x² - 17x - 15 = 0

x = 5           (5,0)

x = -3/4           (-3/4,0)

Find The 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

Find the vertex of y=5x²+4x+3

(-2/5, 11/5)

500

The graph of y = 2x² + 8x - 5 is shown. If the graph contains the point (-6, y), what is the value of y?

y=19 so the point is at (-6,19)