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

Fill in the Blanks

A golf ball is hit off the ground and is modeled by the quadratic equation $h\left(t\right)=-5t^2+30t$  . When does the ball hit the ground again?

seconds

Fill in the Blanks

Given the following quadratic equation, what is the discriminant?

$y=x^2-x-7$  

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

• $$y=-3\left(x+3\right)^2+3$$  

• $$y=3\left(x+3\right)^2+3$$  

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

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

Fill in the Blanks

A rocket is launched from the top of a building. The height (in meters) is given by $h\left(t\right)=-6t^2+30t+30$  , with time, t, in seconds. How long does it take for the rocket to hit the ground? Round your answer to the nearest hundredth (2 places).

seconds

Fill in the Blanks

A rocket is launched from the top of a building. The height (in meters) is given by $h\left(t\right)=-6t^2+30t+30$  , with time, t, in seconds. How high is the rocket after 3 seconds? (It should be a whole number)

meters

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!​