Algebra I Exam 2 Review

Slope

100

What is the slope formula through the points (x₁,y₁) and (x₂,y₂)?

m= (y₂-y₁)/(x₂-x₁)

200

Find the slope of a line through the points (7, 8) and (9, 10).

m = 2/2 = 1

300

What is the slope-intercept equation?

y = mx + b

400

What is the point-slope equation of a line?

y - y₁ = m (x - x₁)

500

Find the x-intercept and y-intercept for the equation 

3x + 9y = 27. Write as points with both coordinates.

x-intercept: (9,0)

y-intercept: (0,3)

Functions & Exponents

100

If f(x) = 4x + 2, what is f(3)?

f(3) = 4(3) + 2 = 14

200

Simplify the expression: 2m² * 5m⁴

10m⁶

300

Simplify the expression: (15a⁹b³)/(5a⁴b²)

3a⁵b

400

Simplify the expression: (4xy³)²

16x²y⁶

500

Rewrite the expression without using a negative exponents: 5^-4

1/5⁴ = 1/625 = 0.0016

Polynomials

100

Multiply the polynomials: 4x² * 5x⁵

20x⁷

200

Use the FOIL or Box Method:

(x+4)(x+6)

x² + 10x + 24

300

Factor out the Greatest Common Factor: 21x⁴ - 3x²

3x²(7x² - 1)

400

Factor with a = 1: x² + 2x - 24

(x + 6)(x - 4)

500

Factor with a >1: 3x² - 2x - 5

(x + 1)(3x - 5)

Quadratics

100

The graph of a quadratic function is called a ___________.

parabola

200

The formula for finding the axis of symmetry is ___________________.

x = -b/2a

300

The formula for finding the discriminant is __________.

b² - 4ac

400

How do you find the coordinates of a vertex?

Find the axis of symmetry (i.e. x-coordinate), and then plug the x-value back into the equation to get the y-coordinate.

500

What is the Quadratic Formula?

x = "negative "b," plus or minus the square root of "b" squared minus four "ac," all over "2a" "

Systems of Equations

100

How would I solve this problem using substitution?

y = 2x + 3

y = 4x + 5

Set the two equations equal to each other.

200

How would I solve this system of equations?

y = -3x + 5

5x - 4y = -3

Plug -3x + 5 into the y-value of the second equation.

300

What would I do to solve this system of equations using elimination?

-4x - 2y = -12

4x + 8y = -24

Cancel the "x" terms and then add the equations. Solve for y. Plug y into one of the original equations to find x.

400

How would I solve this system of equations using elimination?

x - y = 11

2x + y = 19

Cancel the y terms and then add the equations. Solve for x, and then plug x into one of the original equations to solve for y.

500

How would I solve this system of equations?

8x + 4y = 12

-4x + 5y = 17

Multiply the second equation by 2. Add the equations together. Solve for y. Then plug that value into one of the original equations to solve for x.