Unit 7: Quadratic Functions Review

Graphing Quadratics

At the end of the lesson, student should be able to:

• Review the characteristics of Quadratic Functions.

• Graph quadratic Functions using Desmos Calculator.

• Solve for the zeros of quadratic functions.

​WATCH THE FOLLOWING VIDEO

​Write down key information about graphing quadratics.

​You should be able to use your notes to summarize the process for graphing a quadratic function.

Next you will be asked to try a few things on your own.

Make sure you have given the video​ the appropriate attention so that you can be successful.

There are also helpful explanations included.

We will complete an activity when I see you.

​YES...THIS IS GOING IN THE GRADE BOOK!

Explanation Slide...

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Multiple Choice

Find the axis of symmetry for

f(x) = x²- 4x + 5.

• x = -2

• x = 2

• y = 2

• y = -2

• y= 2x +1

Explanation Slide...

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Multiple Select

 Find the x-intercepts for the quadratic function: $$f\left(x\right)=x^2+5x+6$$

• (3,0)

• (2,0)

• (6,0)

• (-2,0)

• (-3,0)

Explanation Slide...

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Multiple Choice

What are the real roots (solutions) of the quadratic y = 2x²+4x+5

• (−1, 3)

• (0,5)

• (5,0)

• (3,-1)

• No real roots

Explanation Slide...

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Multiple Select

Identify the equation for the graph.

• $$y=x^{2\ }-8x+12$$

• $$y=x^{2\ }+6x+2$$

• $$y=\left(x-2\right)\left(x-6\right)$$

• $$y=\left(x+2\right)^{\ }\left(x+6\right)$$

• $$y=x^2+8x+12$$

Explanation Slide...

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Multiple Select

What is the equation for the graph above?  Choose all that apply:

• $$y=x^2+6x+8$$  

• $$y=\left(x-3\right)^2-1$$  
  

• $$y=\left(x-2\right)\left(x-4\right)$$  

• $$y=x^2-6x+8$$  

• $$y=\left(x+2\right)\left(x+4\right)$$  

Multiple Choice

Does this parabola have a maximum or minimum?

• Maximum
• Minimum

Let's use Desmos to analyze and evaluate Quadratic Application Functions.

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Quadratic Application Problems

Multiple Choice

An object's path is modeled by: $$h\left(t\right)=-16t^2+150t+100$$   WHAT is the max height?

• 451.6 feet

• 4.7 feet

• 100 feet

• 10 feet

Make sure you can find the following on your graph. The next 3 slides will ask for this information.

• y-intercept (starting height)

• Vertex (time, max height)

• x-intercept (time, on the ground)​

Multiple Choice

What is the initial height of the object?

• 22

• 48

• 16

• 0

Multiple Choice

How long did it take to reach the max height?

• 12 seconds

• 58 seconds

• 3.5 seconds

• 1.5 seconds

Multiple Choice

How long was the object in the air?

• 2.8 seconds

• 3.4 seconds

• 1.5 seconds

• 8 seconds

Multiple Choice

A raft is dropped from a helicopter 256 feet in the air above the ocean.  Its approximate height, h, after t seconds is given by the function h(t) = -16t² + 256.  How many seconds did it take the raft to hit the water? 

• -4

• 2

• 4

• 8

Multiple Choice

Fireworks are fired from the roof of a 100-foot building. The equation h = -16t² +84t + 100 models the height, h, of the fireworks at any given time, t. How high do the fireworks get?

• 2.625

• 6.25

• 100

• 200

• 210.25

Multiple Choice

Fireworks are fired from the roof of a 100-foot building. The equation h = -16t² +84t + 100 models the height, h, of the fireworks at any given time, t. How high are the fireworks after 1 second?

• 136

• 96

• 168

• 210

• 210.25

Multiple Choice

What is the initial (starting) height of an object following this path? 

h(t) = -16t² +20t + 6

• -16 feet 

• 0 feet

• 20 feet 

• 6 feet 

Zeros of Quadratic Equations

Graphing and finding the Zeroes Quadratic Functions Lesson

Zeroes of Quadratic Equations

Where the graph HITS the X-AXIS

Fill in the Blanks

If there is only an equation given, type the equation into the calculator and look at the graph

Look to see where the graph hits the x-axis

Multiple Choice

What are the zeroes of the equation

$$y=3x^2-3x-6$$  

• -1 and -2

• 1 and -2

• -1 and 2

• 1 and 2

Multiple Choice

What are the zeroes of the equation

$$0=x^2+2x-8$$  

• -4 and 2

• -4 and -2

• -8 and 0

• -8, -4, and 2

X-intercepts are special!

They can also be called ZEROS

However, y-intercepts do not have any other names.

Finding x-intercepts

• Graph- Look to see were the graph crosses the x-axis

• Table- Find a value where y=0 (opposite)

• Equation- Use DESMOS! Then look at the graph

Multiple Choice

Which is a zero of the graph?

• 0

• -1

• 1.5

• -3

Multiple Choice

What are the zeros of the quadratic function?

y = x² - 2x - 15

• x = -2

  x = -15

• x = -3

  x = 5

• x = 3

  x = -5

• x = 1

  x = -16

Multiple Choice

Give the x-intercept

3x + 8y = 24

• (8, 0)

• (0, 8)

• (3, 0)

• (0, 3)

Multiple Select

f(x) = ax² + bx + c

Which statements are true about this form of the quadratic function?

{mark all that apply}

• It is standard form

• It is factored form

• (0,c) indicates the y-intercept

• +a or -a tells us its opening direction

Multiple Select

f(x) = 5x² - 2x - 3

Convert to factored form to identify all true statements

• Parabola opens upward

• Parabola opens downward

• Contains (-3/5, 0) and (1,0)

• Contains (0,-3)

• Contains ( 3/5, 0) and (-5, 0)

Multiple Choice

What are the zeros of the parabola? 

• 1, 5
• 3, -5 
• 3, 0
• -6, 1