Solving Quadratic Equations

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 - 6x + 5 = 0

x = 5 x = 1

300

The zeros of a quadratic function are -6 and 7. What could the function be? Give 2 functions.

f(x) = (x+6)(x-7)

f(x) = x²-x-42

f(x) = gcf * (x²-x-42)

400

Solve the following quadratic equation by factoring. 3x² - 6x - 24 = 0

x = 4 x = -2

500

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

x = -1/2 x = 3

Square Roots

100

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

+11 or -11

200

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

x = 10 x = -10

300

What is an approximate x value for the equation y= 2x² + 8 when y=12?

x=+- sqrt(2)= +-1.41421356237

400

Determine the solutions of (3x-2)²=49

x = 3 x = -5/3

500

Danny is building a wheelchair ramp. He draws a right triangle with legs x and x-2 and a hypotenuse of 2x-6. What is the value of x? (HINT USE PYTHAGOREAN THEOREM)

x=4

Completing the Square

100

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

x = -2 x = -4

200

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

x = 1 x = 5

300

Susan rewrote the equation x² - 2x - 24 = 0 so that she can solve by completing the square. What equation could she have written? (Hint: this is the step where you complete the square)

(x-1)^2 = 25

400

Determine the solutions of 2x² + 12x - 42 = 0 by completing the square.

x = -3 +- sqrt(30) = 2.48, -8.48

500

Complete the square to find the minimum value of the function  y= 2x² - 8x - 10

x = -1, x=5

Quadratic Formula

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 x = -5

300

Solve the following quadratic equation by using the quadratic formula: x² - 3x = 13

x = (3 + sqrt(61))/2 = 5.41 x = (3 - sqrt(61))/2 = -2.41

400

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

x = -1/2 x = -4

500

What is the discriminant of the equation 4x² - 10x - 1 = 0 and how many real solutions does the equation have?

116; 2 solutions

Understanding Graphs/Linear Quad Systems

100

Find the vertex of f(x)=5x²+2x-2

(-1/5,-11/5)

200

What is a line that intersects the parabola y = x² - 3x +4 at two points?

Answers vary

Ex: y=-3x+5

300

Determine the solutions of the system of equations: 

y=2x+2

y=x²+10x+2

(0,2)

(-8,-14)

400

What are key features of the function f(x)=-x²-4x?

x intercepts? y intercept?

vertex?

domain? range?

(0,0), (-4,0)

(-2,4)

all real numbers; y<4

500

A hot dog stand models their profit using the function P(x) = -5x² + 25x - 30 where x is the number of hot dogs sold, in thousands, and P(x) is the profit in dollars. How many hot dogs will maximize the profit?

x= 2500 hot dogs