| 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, complete the square for each quadratic expression in order to form a perfect square trinomial. |
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1) What is the completed perfect square for the given quadratic expression?
Hint: Take 1/2 of the coefficient of the linear term and square it. |
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| 2) What is the completed perfect square for the given quadratic expression? |
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| 3) What is the completed perfect square for the given quadratic expression? |
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4) What is the completed perfect square for the given quadratic expression?
Hint: The coefficient of x is understood to be 1. |
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In the following problems, solve each problem by completing the square.
Remember: In this process, take 1/2 of the coefficient of the linear term and square it to find a perfect square trinomial. Then, add the number to both sides of the equation to keep the equations in balance. Continue on to solve the equations for x. |
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| 5) Complete the square and solve for x. |
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| 6) Complete the square and solve for x. |
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7) Complete the square and solve for x.
Hint: Switch the sides of the equation. The value of the equation will remain the same. |
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8) Complete the square and solve for x.
Hint: Since all factors are multiplied by 2, divide both sides by 2 to determine a simplified equivalent equation. |
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| In the following problems, use the quadratic formula to solve each equation. Make sure that the quadratic equation is expressed in standard form before beginning the problem. |
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| 10) Solve for x. |
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| 11) Solve for x. |
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| Graphing Quadratic Functions |
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| 12) Which of the quadratic functions has the narrowest graph? |
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| 13) What are the coordinates of the vertex? Is the vertex a maximum or minimum value? |
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| 14) How does the translated function compare to the parent function? |
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| 15) The parent function f (x) is reflected across the x-axis, vertically stretched by a factor of 2, and translated 5 units to the left to create g(x). What is the quadratic equation for g(x)? |
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| In the following questions refer to the given function. Sketch a graph of the function on paper, and then answer the questions. |
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| 17) What is the vertex and axis of symmetry of the function? |
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18) Does the function have a maximum or minimum value and what is that value?
Hint: Consider a. |
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19) State the domain and range of the function.
Consider:
-The domain is all possible x-values of the coordinates of the points on the parabola.
-The range is all possible y-values of the coordinates of the points on the parabola. |
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| In the following questions refer to the given function. Sketch a graph of the function on paper, and then answer the questions. |
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| 20) What is the vertex and axis of symmetry of the function? |
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| 21) Does the function have a maximum or minimum value and what is that value? |
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| 22) State the domain and range of the function. |
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| Write Quadratic Functions in Vertex Form |
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| In the following problems, transform each of the given functions into vertex form, and then select the correct vertex form from the choices shown below. |
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| 23) What is the vertex form for the given function? Choose from the answer choices above. |
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24) What is the vertex form for the given function? Choose from the answer choices above.
Hint: Use completing the square to put the function in vertex form. |
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| 25) What is the vertex form for the given function? Choose from the answer choices above. |
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Review
The following problems are a review of matrices. |
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26) For the given matrices, find 2A – 3B. Give the answer by stating the rows of the new matrix.
Click here to review the unit content explanation for Matrices. |
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27) Multiply the matrices. Give the answer by stating the rows of the new matrix.
Click here to review the unit content explanation for Matrices. |
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28) Multiply the matrices. Give the answer by stating the rows of the new matrix.
Click here to review the unit content explanation for Matrices. |
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29) True or False. Matrix multiplication is commutative.
Hint: Consider the results of the last two problems.
Click here to review the unit content explanation for Operations with Numbers and Exponents. |
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30) Multiply the matrices. Give the answer by stating the rows of the new matrix.
Click here to review the unit content explanation for Matrices.
Hint: Remember to perform multiplication and addition by working rows over columns.
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| 31) 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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