Unit 3 Review (Algebra 2)

​Unit 3 Review

Algebra 2​

Sections in Unit 3:​

• 3.1 Quadratic Applications

• 3.2 GCF and Trinomial Factoring (a=1)

• 3.3 Trinomial Factoring (a not 1)

• 3.4 Solving Quadratics by Factoring/Graphing

• 3.5 Solving via Square Roots (weird formats)

• 3.6 Completing the Square

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• 3.7 The Quadratic Formula

• 3.8 Quadratic Formula Applications

• 3.9 Graphing using Vertex Form

• 3.10 Standard to Vertex Form

• 3.11 More Detailed Graphs

Multiple Choice

Factor completely:

$$x^2-3x-18$$  

• $$\left(x+3\right)\left(x+6\right)$$  

• $$\left(x-6\right)\left(x+3\right)$$  

• $$\left(x-3\right)\left(x-6\right)$$  

• $$\left(x-3\right)\left(x+6\right)$$  

Multiple Choice

Factor completely:

$$4a^2-64a$$  

• $$4a\left(a-4\right)$$  

• $$\left(4a-1\right)\left(a-16\right)$$  

• $$\left(a-4\right)\left(a-16\right)$$  

• $$4a\left(a-16\right)$$  

Multiple Choice

Factor completely:

$$16x^2-25$$  

• $$\left(4x-1\right)\left(4x+25\right)$$  

• $$\left(4x+5\right)\left(4x+5\right)$$  

• $$\left(4x-5\right)\left(4x+5\right)$$  

• $$\left(4x-5\right)\left(4x-5\right)$$  

Multiple Choice

Factor completely:

$$12x^2+5x-3$$  

• $$\left(3x-1\right)\left(4x+3\right)$$  

• $$\left(3x+3\right)\left(4x-1\right)$$  

• $$3\left(x-1\right)\left(4x+3\right)$$  

• $$\left(4x-3\right)\left(3x+1\right)$$  

Multiple Choice

The quadratic $$x^2-7x-30=0$$   factors into $$\left(x-10\right)\left(x+3\right)=0$$  . What are the roots?

• x = -7, -30

• x = 10, -3

• x = -10, 3

Multiple Choice

Given the previous discriminant, are the roots of that equation real or imaginary?

• Real

• Imaginary

Multiple Choice

Solve the following quadratic equation:

$$x^2+5x+2=0$$  

Hint: It does not factor.

• $$x=\frac{-5\pm\ \sqrt[]{17}}{4}$$  

• $$x=\frac{5\pm\ \sqrt[]{21}}{2}$$  

• $$x=\frac{-5\pm\ \sqrt[]{17}}{2}$$  

• $$x=\frac{-5\ \pm\ \sqrt[]{33}}{2}$$  

Multiple Choice

Solve:

$$5x^2=125$$  

• x = 5, -5

• x = 5

• x = -5+i, -5-i

• x = 25, -25

Multiple Choice

Which technique would be the most efficient to solve the following equation?

$$7x^2=29x$$  

• Factoring via GCF

• Factoring via Grouping / Mr. Jones' Method

• Square Root

• Quadratic Formula

• Complete the Square

Multiple Choice

Essentially ANY quadratic equation has how many roots/solutions?

• None

• 1

• 2

• 3

Multiple Choice

What type/how many roots does the shown quadratic have?

• 2 imaginary

• 1 real, 1 imaginary

• 2 real

• 3 real

Multiple Choice

The following equation represents what translations from the parent?

$$y=\left(x+5\right)^2-1$$  

• 5 right, 1 up

• 5 left, one up

• 5 right, 1 down

• 5 left, 1 down

Multiple Choice

Based on opening UP/DOWN, which equation COULDN'T possibly represent the graph?

• $$y=-x^2+5x+8$$  

• $$y=x^2+5x+8$$  

• $$y=x^2-5x-8$$  

• $$y=x^2-5x+8$$  

Multiple Choice

What is the axis of symmetry of $$y=-\left(x-7\right)^2+3$$  ?

• x = 3

• x = -7

• x = -3

• x = 7

Multiple Choice

Does the following function have a maximum or a minimum?

$$y=-\left(x-7\right)^2+3$$  

• maximum

• minimum

• Can't be determined

Multiple Choice

The following function is the same function written in two forms:

Standard Form: $$y=x^2-8x+7$$  

Vertex Form: $$y=\left(x-4\right)^2-9$$  

What is the vertex?

• (2, -9)

• (4, -7)

• (4, -9)

• (8, -7)

Multiple Choice

The following function is the same function written in two forms:

Standard Form: $$y=x^2-8x+7$$  

Vertex Form: $$y=\left(x-4\right)^2-9$$  

What are the x-intercepts?

• x = 1, 7

• x = -1, -7

• x = 8, -2

• x = 4, -9

Multiple Choice

The following function is the same function written in two forms:

Standard Form: $$y=x^2-8x+7$$  

Vertex Form: $$y=\left(x-4\right)^2-9$$  

What is the y-intercept?

• y = -7

• y = -9

• y = 7

• y = 4

Multiple Choice

What are the roots of the quadratic function?

• x = 2, 5

• x = 7

• x = -2, 5

• There are none

Multiple Choice

How long does it take the ball to hit the ground?

• 4 seconds

• 80 seconds

• 1.5 seconds

Multiple Choice

Write the following Standard Form Quadratic into Vertex Form by completing the square.

$$y=x^2-10x+7$$  

• $$y=3x^2-20x+1$$  

• $$y=\left(x+5\right)^2+18$$  

• $$y=\left(x-5\right)^2-18$$  

• $$y=\left(x-5\right)^2+32$$  

Multiple Choice

Use any of the following features to determine the correct equation for the provided graph:

Vertex, axis of symmetry, roots/x-ints, y-int

• $$y=-3\left(x+3\right)^2+3$$  

• $$y=3\left(x+3\right)^2+3$$  

• $$y=\frac{1}{3}\left(x-3\right)^2+3$$  

• $$y=-\frac{1}{3}\left(x-3\right)^2+3$$  

That's it!​

• ​Use this presentation as a "simulation" of the test!

• If parts of it didn't go well, do something about it!

• You can retry the practice version in Canvas as much as you'd like!​