Algebra 2 Final

PEMDAS/ Solve for x

100

[(14 + 3) + (20/2)²] + 5

122

200

[(10 - 3)² + 7] - 4 + 6²

88

300

(11 + 2)/(y + 5) = 1

y = 8

400

12 + (y/11) = 8

y = -44

500

10*(8 + y) = 190

y = 11

Linear Equations

100

Find the slope between the points (1, -4) and (-2, 5)

m = -3

200

Fins the slope between the points (0, 2) and (3, 4)

m = 2/3

300

Find the y-intercept of a line where the slope is 2 and passes through the point (3, -2)

b = -8

400

Find the equation of a line that has a slope of -2/3 and passes through the point (1, 3)

y = 2/3 x + 11/3

500

Write the equation of the line that has a slope of -3/5 and passes through the point (4, -2)

y = -3/5 x + 2/5

Systems of Equations

100

Solve using substitution:

7x - 4y = -7

5x + y = 22

x = 3

y = 7

200

Solve using substitution

x - 5y = 21

-6x = 24

x = -4

y = -5

300

Solve using elimination

-2x - 17y = 11

4x - 13y = 25

x = 3

y = -1

400

Solve using elimination

2x + y = 10

3x - 2y = 15

x = 5

y = 0

500

Solve using any method

7x + 5y = 5

-7x + 12y = 12

x = 0

y = 1

Functions

100

If f(x) = 3x + 2 and g(x) = x +5, what is f-g(x)?

2x - 3

200

If f(x) = 5x - 8 and g(x) = x² - 7x + 6, what is f+g(x)?

x² - 2x - 2

300

If f(x) = 3x + 2 and g(x) = x + 5, what is f∘g(x)? 

3x + 17

400

If f(x) = 3x + 2 and g(x) = x + 5, what is g∘f(x)? 

3x + 7

500

If the parent function is f(x) = x², what would the equation be if it is shifted 2 units to the left and 1 unit down?

f(x) = (x + 2)² -1

Quadratics

100

Find the roots using square roots

3x² = 48

x = +/- 4

200

Find the roots by completing the square:

x² + 2x - 8 = 0

x = -4, 2

300

Solve by factoring:

x² - 2x - 15 = 0

x = -3, 5

400

Solve using the quadratic formula:

4x² - 20x + 24 = 0

x = 3, 2

500

Solve using the quadratic formula. Write the answer in a+bi form.

x² - 6x + 25 = 0

x = 3 +/- 4i