| Some activities may require making graphs on paper. Click here to view and print graph paper, as needed. |
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| In the following problems, show that the function is a quadratic function by expressing it in the standard form shown below. |
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1) What is the standard form for the function?
Hint: Use FOIL to multiply the two binomials. |
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2) What is the standard form for the function?
Hint: FOIL the two binomials first; then, multiply all terms by –3. |
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| In the following problems, determine if the function is a quadratic function. |
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| 3) True or False? The function is a quadratic. |
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| 4) True or False? The function is a quadratic. |
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5) True or False? The function is a quadratic.
Hint: Express the function in standard form first. |
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6) For the given quadratic,
(a) state whether the parabola opens upward or downward and
(b) state whether the y-coordinate of the vertex is the minimum value or the maximum value of the function. |
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| In the following problems, determine if the parabola opens upward or downward and if the y-coordinate of the vertex is a minimum value or maximum value of the function. |
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7) For the given quadratic,
(a) state whether the parabola opens upward or downward and
(b) state whether the y-coordinate of the vertex is the minimum value or the maximum value of the function.
Hint: Express the function in standard form first. |
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8) For the given quadratic,
(a) state whether the parabola opens upward or downward and
(b) state whether the y-coordinate of the vertex is the minimum value or the maximum value of the function. |
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9) Solve the quadratic equation by graphing.
Hint: Graph the parabola and find the points where the graph crosses the x-axis. |
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| In the following problems, solve for x by isolating the squared term or expression; then, taking the square root of both sides of the equation. |
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| 10) Solve for x. |
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| 11) Solve for x. |
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12) Solve for x.
Hint: To begin, isolate the squared expression by undoing the subtraction of 8 and undoing the multiplication by 4. |
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| In the following problems, factor each quadratic expression. Check the answers by using the distributive property or the FOIL method, whichever is appropriate for the problem. |
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| In the following problems, solve for x by factoring and applying the Zero Product Property. There will be two solutions for each problem. |
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| 21) A ship in distress launches a flare upward with a velocity of 176 feet per second. The height (h) of the flare is given by the function provided below in relation to the time (t) the flare travels. |
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| Solving Quadratic Equations |
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In the following problems, solve for x by completing the square.
Recall: To complete the square, take 1/2 of the linear term, square it, and then add it on. Also, be sure to keep the equation in balance. |
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| 22) Solve for x. |
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23) Solve for x.
Hint: To begin, factor a 2 from both the quadratic and linear term. |
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| In the following problems, solve for x by using the quadratic formula. |
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25) Solve for x using the quadratic formula.
Hint: Express the equation in standard form first. |
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| 26) What transformation of the parent function is the given function? |
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| 27) What function is a transformation of the given parent function after it has been translated 3 units up and 2 units to the right? |
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| In the following problems, express the quadratic function in vertex form as shown below by using the completing the square method and keeping the equation in balance. |
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28) What is the vertex form for the given quadratic function?
Hint: To begin, factor a 2 from both the quadratic and linear term. |
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29) What is the vertex form for the given quadratic function?
Hint: The negative sign in front of the squared term indicates that a (–1) is a factor of the term. To begin, factor a (–1) from both the quadratic and linear term. |
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| 30) Identify the vertex (x, y) and the axis of symmetry (x = h) for the quadratic graph. |
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31) For the graph in the previous problem,
(a) what is the domain and
(b) what is the range?
Hint: The domain is all possible x-values of the function. The range is all possible y–values of the function. |
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In the following problems,
(a) find the discriminant of the quadratic function and
(b) determine the type and number of solutions (two imaginary solutions, two real solutions, or one real solution) for the quadratic equation. |
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| 32) (a) What is the discriminant? (b) What is the type and number of solutions? |
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| 33) (a) What is the discriminant? (b) What is the type and number of solutions? |
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| In the following problems, perform the indicated operation for the complex numbers and simplify. |
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34) Simplify.
Hint: Begin by factoring (–1)(48). |
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| 35) What is the value of the given power of i ? |
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36) What are the solutions for the given quadratic function?
Hint: Use the quadratic formula. |
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40) Rationalize the denominator of the given complex number.
Hint: Multiply the numerator and the denominator by the conjugate of the denominator. |
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| 41) 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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