Math Review Game Project

The Quadratic Formula

100

x² + 4x + 13 = 6x + 24

X = 1-2√ 3

x = 1+2√ 3

200

4x² + 8x - 3 = -2x² + 7x - 1

x = 1/2 

x = -2/3

300

x² - 5x + 6 = 0

x=2 and x=3

400

2x² + 7x - 4 = 0

x = 1/2 

x = -4 

500

3x² - 2x + 5 = 0

x = 1±i√ 14 / 3

Solving Cubic functions by Finding the Roots

100

2³

8

200

(5y)³

125y³

300

Find all roots by factoring: 

x³ - 1000 = 0

-5± 5i√3

400

Find all roots of the equation:

x³ - 6x² + 11x - 6 = 0

Roots: x = 1, 2, 3

500

Find all roots of the equation:

x³ - x² - 9x + 9 = 0 

Roots: 1, 3, -3

Multiplicities of Roots

100

List the roots and their multiplicities: 

f(x) = -2/3x(x - 3)²(x + 4)³

x = 0, M1

x = 3, M2

x = -4, M3

200

List the roots and their multiplicities:

f(x) = x²(2x - 3)(x + 7)

x = 0, M2

x = 3/2, M1

x = -7, M1

300

Find the lead coefficient of each polynomial function. Then describe the end behavior using limit notation:

f(x) = (2x - 3)²(x - 5)

LC: 4 pos

D: 3 odd

limf(x)= -∞     limf(x)= ∞ 

400

What is the leading coefficient, and what is the end behavior?

f(x) = -3x⁴ + 5x² - 8

LC: -3 neg

D: 4 even

limf(x)= -∞                        limf(x) = -∞ 

500

What is the leading coefficient, and what is the end behavior?

f(x) = 1/2x⁵ - 7x³ + x + 9

LC: 1/2 

D: 5 odd

limf(x)= ∞ 

limf(x)= -∞ 

Quadratic Functions in Vertex Form

100

Find the coordinates of the vertex, determine whether it's a max/min, and write the equation for the axis of symmetry. 

f(x) = 2(x - 4)² + 3

Vertex: (4,3)

Minimum

AOS: (-4, 3)

200

Find the coordinates of the vertex, determine whether it's a max/min, and write the equation for the axis of symmetry. 

f(x) = -(x - 2)² - 2

Vertex: (2, -2)

Maximum

AOS: (-2, -2)

300

Identify the vertex and axis of symmetry of the quadratic function:

f(x) = (x - 3)² + 5

Vertex: (3, 5)

AOS: x = 3

400

Determine the vertex, axis of symmetry, and whether the parabola opens up or down:

f(x)= -2(x + 4)² - 1

vertex: (-4, -1)

AOS: x = -4

Since a = -2, the parabola opens downward

500

Find the vertex, axis of symmetry, and maximum or minimum value of the function:

f(x) = 1.2(x - 6)² + 2

Vertex: (6, 2)

AOS: x = 6

Since a = 1/2 > 0, the parabola opens upward 

Solving Exponential Equations

100

Solve for x:

3⁴ = 3^{2x + 1}

x = 3/2

200

Solve for x:

7^x = 7^{2x^2 -1}

x = 1/2

x = 1

300

Solve the equation:

4^x+1 = 64^x-1

x = 2

400

Solve the equation:

3^2x - 10(3^x) + 9 = 0

x = 0

500

Solve the equation:

8^x + 2^{3x + 1} = 192

x = 2