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4.4 Quadratic Equation Review (Due 1/29/24)

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Last updated about 2 months ago
14 questions
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10
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10
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10
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8
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4
A.APR.3
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12
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3
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10

Essential Question: What are other methods of solving quadratic functions besides factoring?


Learning Target: Students will be able to solve quadratic equations using the completing the square method to model real-world situations.


Show your work for credit.

Simplifying Radicals

Question 1
1.

Simplify this radical.

Completing the Square: Rational Solutions

Question 2
2.

Use Completing the Square to solve this quadratic equation. Give all solutions in simplest form.

Question 3
3.

Use Completing the Square to solve this quadratic equation. Give all solutions in simplest form.

Completing the Square: Irrational Solutions

Question 4
4.

Use Completing the Square to solve this quadratic equation. Give all solutions in simplest form.

Question 5
5.

Use Completing the Square to solve this quadratic equation. Give all solutions in simplest form.

Quadratic Equation Review

Question 6
6.

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Question 7
7.

Use Your Vocabulary: Match each zero with its graph(s).

  • -1
  • 1
  • 2
  • -2
Question 8
8.

  • The springboard was 14 feet high.
Question 9
9.

Question 10
10.

Match each equation to its graph

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f(x) = (x - 2)(x - 4)
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f(x) = -(x + 2)(x - 2)
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f(x) = (x + 2)(x - 4)
Question 11
11.

Factor this quadratic function:
x2 - 3x - 4

Question 12
12.

Factor this quadratic function:
x2 + 3x - 10

Question 13
13.

Factor this quadratic function:
2x2 - 13x - 7

Question 14
14.

Factor this quadratic function:
4x2 - 15x - 25

Match the graphs with their negative regions (below the x-axis).
(-1, 3)
(-∞, -1) and (3, ∞)
(-3, 1)
(-∞, -3) and (1, ∞)
(-2, 4)
(-∞, -2) and (4, ∞)
(-4, 2)
(-∞, -4) and (2, ∞)
A swim team member performs a dive in the pool from a springboard.
The parabola below shows the path of her dive. Use the graph to answer the sorting question below.



Sort each statement into agree or disagree (based on the graph above)
The diver’s height was
decreasing the entire time.
The diver reached her
maximum height at 23 feet in the air.
The diver landed in the water about 14 feet away from the springboard.
The diver’s range was between 0 and 23 feet.
The diver is going up in the air
between 0 < x < 3.
The diver was 4 feet away from the springboard when she reached her maximum height.
Between 3 feet from the springboard and 8 feet from the springboard, the diver’s height was decreasing.
When the diver was 5 feet away from the springboard, she was 19 feet high.
Using the graph, f(2) = 22.
The diver was again at the height of the springboard 6 feet away from the board.
The diver’s height was changing at a faster rate between 4 feet and 6 feet from the springboard versus 6 feet and 8 feet from the springboard.
Agree
Disagree
Match the statement to the quadratic equation it is describing.
The zeros of my parabola are (-6, 0) and (-2, 0).
My y-intercept is 5
and my vertex is (-2, 1).
My function's y-intercept and vertex are the same.
The range of my function is y ≤ 1.
Find my function using the clue below:
f(-1) + f(4) = -11
My minimum is y=1 and
all the y-values of my function are positive.
The x-intercepts of my parabola are opposites.
My function has a vertex that is (0, 0) and an axis of symmetry of x = 0.
My function is decreasing over the interval (-4, ∞).
My function is only increasing over the interval x > -1.
For my function, f(x) is negative when
x < 0 and x > 2.
I have an axis of symmetry of x = -1.