So you think you can Algebra?

Forms of Linear Equations

100

Slope-intercept form of a linear equation:

y = mx + b

200

Standard form of linear equation:

Ax + By = C

300

Point-slope form of linear equation:

Hint - this equation form includes an x₁ and y₁

y - y₁ = m(x - x₁)

400

Use the point-slope equation [y - y₁ = m(x - x₁)] to find the slope-intercept form of the linear equation.

m = -1

(3, -2)

y - (-2) = -1(x - 3)

y + 2 = -1x + 3

y = -1x + 1

500

Translate the slope-intercept equation into standard form:

y = 3/4x - 5

Hint: Ax term can't be negative or fractional

3x - 4y = 20

Equations/Systems of Equations

100

Solve:

Seven subtracted from the product of four and a number is 37

4x - 7 = 37

x = 11

200

Solve using substitution:

y = 2x - 1

2x + 3y = -7

(-1/2, -2)

300

Solve:

3(x - 2) - (x - 6) = 4(x - 7)

x = 14

400

Solve using elimination (addition)

2x + 3y = 20

-2x + y = 4

(1, 6)

500

Solve:

3/4x - 2/3 = 5/6

x = 2

Monomials, Binomials, Trinomials, and Polynomials

100

Classify the expression:

3x³ + 2x - 1

Cubic Trinomial

200

Simplify:

2x² - 5x - xy - x³ + 4 - x² + 3x + 4x³ + 3 + xy

3x³ + x² - 2x + 7

300

4x³(x³/x⁵) - 5xy/y

-x

400

(4x²)³(2x)²

64x⁶(4x²)

256x⁸

500

Simplify:

(2x²y)(3x²)/8x⁶

6x⁴y/8x⁶

3y/4x²

Linear & Exponential Functions

100

An equation with an output and an input.

Function

200

The name for rate of change of a line.

Slope

300

How do you know if an exponential relationship is increasing?

Hint: b

b>1

400

The letter to symbolize where a LINE crosses the y-axis.

b

500

f(x) = 2x - 7

find x, when f(x) = -8

-8 = 2x - 7

-1 = 2x

-1/2 = x

Quadratic Functions

100

What do quadratic functions create when graphed?

A parabola

200

Find the axis of symmetry:      x = -b/2a

x² + 12x + 32 = 0

-(12)/2(1) = -6

x = -6

300

Find the vertex, give final answer as (x, y):

3x² - 6x + 1 = 0

-(-6)/2(3) = 6/6 = 1

3(1)² - 6(1) + 1 = 0

Final answer: (1, -2)

400

Find the discriminant of the quadratic function:

d = b² - 4ac                     9x² + 6x + 6 = 5

Does the function have 0, 1, or 2 solutions?

d = 0

1 SOLUTION

500

Find the zeros of the function by factoring:

5x² + 17x - 12 = 0

x = {-4, 3/5}