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| Introduction to Quadratic Functions |
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| In the following problems, determine if the function is quadratic. |
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| 1) True or False? This function represents a quadratic equation. |
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| 2) True or False? This function represents a quadratic equation. |
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| 3) True or False? This function represents a quadratic equation. |
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| 4) True or False? This function represents a quadratic equation. |
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| In the following problems, multiply the factors (FOIL) and express the function in standard form. |
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| 5) What is the standard quadratic form for the given function? |
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6) What is the standard form for the given function?
Hint: FOIL the two binomials first, and then multiply the product by 2. |
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7) What is the standard form for the given function?
Hint: Apply the distributive property. |
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| 8) What is the standard form for the given function? |
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| In the following problems, state whether the parabola opens up or down, and whether the y-coordinate of the vertex is the minimum value or the maximum value. |
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| 9) Does the parabola open up or down? Is the y-coordinate of the vertex a minimum value or a maximum value? |
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| Solving Quadratic Equations by Graphing |
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| In the following problems, use the related graph of each equation to determine its solutions. If exact roots cannot be found, state the consecutive integers between which the roots are located. |
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| Solving Quadratic Equations |
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In the following problems solve the equation.
Hint: Isolate the "squared" term, then solve the equation by taking the square root of both sides. |
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| 15) Solve the equation for x. |
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| 16) Solve the equation for x. |
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17) Solve the equation for t.
Hint: Begin by taking the square root of both sides, then solve. |
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18) Solve the equation for r.
Hint: Isolate the "squared" expression, then solve the equation by taking the square root of both sides. |
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| Factoring Quadratic Expressions |
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| In the following problems, factor each expression by determining the Greatest Common Factor (GCF) and dividing both terms by the GCF. |
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In the following problems, factor each expression.
Hint: Find two factors of the constant term, that when added together, result in the middle term. |
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24) Is Emily correct? Please explain why or why not.
Hint: Notice that both terms are perfect squares, but they are connected with a minus sign. |
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Zero Product Property
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| Applications of Quadratic Functions |
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29) An arrow is shot upward at an initial velocity of 64 feet per second.
The height of the arrow is given by the function below where h is the height in feet and t is the time in seconds.
a) How long after the arrow is shot does it hit the ground?
b) How long does it take the arrow to reach its maximum height?
c) How high does the arrow go? |
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| 33) If you were directed by your school to complete Offline Activities for this course, please enter the information on the Log Entry form. |
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