Algebra 1

factoring

100

x² + 5x + 6

(x + 2)(x + 3)

200

x² - x - 6

(x - 3)(x + 2)

300

x² + 2x - 15

(x + 5)(x - 3)

400

4x² - 25

(2x - 5)(2x + 5)

500

x³ - 3x² - 4x + 12

(x - 3)(x - 2)(x + 2)

parablas

100

y = (x - 2)² + 3

What is the vertex of the parabola?

Vertex = (2, 3)

200

y = x² + 6x + 8

What is the axis of symmetry?

Axis of symmetry = x = -3

300

y = -2x² + 4x - 1

Find the vertex and determine whether the parabola opens up or down.

Vertex = (1, 1)

Since a = -2 < 0, the parabola opens downward

400

y = x² - 4x + 5

Convert this equation to vertex form and find the vertex.

Vertex form = y = (x - 2)² + 1, Vertex = (2, 1)

500

5. Advanced – Solve a word problem:

A ball is thrown upward and its height in meters after t seconds is given by:

h(t) = -5t² + 20t + 1

What is the maximum height the ball reaches, and at what time does it occur?

Answer: Max height = 21 meters, occurs at t = 2 seconds

simplifiying

100

3x + 5x

 8x

200

2(4x + 3)

8x + 6

300

5x - 3(x - 2)

 2x + 6

400

(2x + 1)(x - 3)

2x² - 5x - 3

500

(x + 2)(x - 4) + (x - 2)(x + 4)

2x² - 16

solving equations

100

2x+5=13

x=4

200

3x−4=2x+7

x=11

300

x²=25

x=5 or 𝑥=−5

400

x²−5x+6=0

x=2 or x=3

500

2x²−3x−5=0

x=2.5 or x=−1

Inequalitys

100

x+3>5

x>2

200

2x−4≤6

x≤5

300

3<2x+1≤7

1<x≤3

400

−2(x−3)>4x+1

x< 5/6

500

3x−7<2x+1

x<8