Math 2 Quadratic Functions Review

Math 2 Quadratic Functions Review

Forms, traits, and graphical characteristics

The parabola...the parent function is the ORIGINAL, pictured in red dots

• How does the blue one move FROM the parent?

• Write the equation of each, using vertex form.

• We'll check together on GM tab.

What about the roots?

What can we conclude about the x-intercepts (zeros or roots) of the blue function? How can you show this algebraically?

Do you remember the quadratic formula?

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Multiple Choice

Which equation best represents the graph?

• y = 2(x - 4)² + 5

• y = 2(x + 4)² + 5

• y = -2(x - 4)² + 5

• y = -2(x + 4)² + 5

Multiple Choice

What are the

x-intercepts of the function

f(x)= (x - 2)(x + 3)?

• x = - 2 or x = 3

• x = 2 or x = -3

• The are no real roots

• x = 2 or x = 3

Multiple Choice

Given f(x) = (x-3)² + 5.  What transformations took place from the original function f(x)?

• Left 3 and up 5
• Right 3 and down 5
• Left 3 and down 5
• Right 3 and up 5

Multiple Choice

Given f(x) = (x-3)² + 5...

What kind of zeros does this function possess?

• 2 real

• 1 real

• none (they are imaginary)

• not enough info

Writing Quadratic Functions

• Pay attention to what you are given

• Zeros? Write factored form.

• Vertex? Write vertex form.

• You can convert to any form from any other form!

Given the zeros?

• Start with factored form.

• This one had to have a maximum, so we had to place a negative out front.

• What is the meaning of "x = -1"?

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Multiple Choice

 $y=-\left(x-2\right)\left(x+4\right)$  Convert to standard form:

•  $y=-x^2-2x+4$  

•  $y=-x^2+2x-8$  

•   $y=-x^2-2x+8$  

•  $y=-x^2+2x+8$  

Multiple Choice

 $y=-\left(x+1\right)^2+9$  Convert to standard form:

•  $y=-x^2-2x+4$  

•  $y=-x^2+2x-8$  

•   $y=-x^2-2x+8$  

•  $y=-x^2+2x+8$  

Where did we get the +9 from?

Fill in the Blank

 $y=2\left(x-1\right)^2+3$  

Where is the vertex of this function? Type the coordinates (use NO spaces).

Fill in the Blank

 $y=2\left(x-1\right)^2+3$  

Where is the y-intercept of this function? Type the coordinates (use NO spaces).

More on that last one...

What is the relationship between the vertex and the axis of symmetry?

And what type of zeros must we assume?

Convert to Vertex Form

• First, vertex form shows the vertex aka how the function SHIFTS from the origin

• Use complete the square to convert from standard form to vertex form

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Multiple Choice

What type of zeros will occur?

• none

• 2 real

• 1 real

Multiple Choice

What is the vertex of the equation

 $y=\left(x+7\right)^2+3$  

• (7, 3)

• (7, -3)

• (-7, 3)

• (-7, -3)

Multiple Choice

Which of the following shows
f(x) = x² + 12x - 2
written in vertex form?

• f(x) = (x + 6)² + 142
• f(x) = (x + 6)² - 34
• f(x) = (x + 6)² - 38
• f(x) = (x + 6)² + 34

Fill in the Blank

The parabola y = x² - 4x + 5 will have a vertex, write as a coordinate (x, y)

Multiple Choice

Which of the following is the description of the transformation of the graph y = (x - 5)² ?

• Shifts right 5.

• Shifts left 5.

• Shifts up 5.

• Shifts down 5.

Multiple Choice

What is the vertex of the equation

 $y=\left(x-3\right)^2+5$  

• (-3, 5)

• (3, 5)

• (-3, -5)

• (3, -5)

Finding Imaginary Zeros

SAME process as solving a quadratic equation and finding solutions, whether they are real or imaginary.

Finding Imaginary Zeros

If we started (or had converted) in vertex form, the process is potentially easier than the quadratic formula!

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Multiple Choice

Complete the square for: x² - 4x - 77 = 0

• (x - 2)² + 73
• (x + 2)² + 73
• (x - 2)² - 81
• (x + 2)² - 81

Multiple Choice

Which graph has the x intercepts of -2 and 1?

• y = 2x -1

• y = x²-2x +1

• y = x²+x-2

• y=x²-x-2

Multiple Choice

What are solutions of the quadratic equation?

y = x² - 2x - 15

• x = -2

  x = -15

• x = -3

  x = 5

• x = 3

  x = -5

• x = 1

  x = -16

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Multiple Choice

What are the zeros of the function f(x) = x² + 64?

• -8 and 8

• -8i and 8i

• (-√8) i and (√8) i

• -√8 and √8

Multiple Choice

Solve x² - 5x + 10 = 0

• (5 - i√15)/2  ,  (5 + i√15)/2
• (5 - √15)/2  ,  (5 + √15)/2
• (5 - i√65)/2  ,  (5 + i√65)/2
• (5 - √65)/2  ,  (5 + √65)/2