Questions

For the first two problems show that the function is a quadratic function by writing it in the form shown below. State the letter of the correct answer.

1) f(x)=(x – 3)(x – 5)

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2) f(x) = –3(x – 11)(x + 1)

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For the next three problems, identify whether or not the function is a quadratic by selecting true or false.

3) Quadratic?

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4) Quadratic?

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5) Quadratic?

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For the next three problems, (a) state whether the parabola opens up or down and (b) state whether the y-coordinate of the vertex is the minimum value or the maximum value of the function.

6) How does the parabola open? Is the vertex a minimum or maximum value?

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7) How does the parabola open? Is the vertex a minimum or maximum value?

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8) How does the parabola open? Is the vertex a minimum or maximum value?

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For the next four problems, solve for “x”. State the answer or the letter of the correct answer choice, whichever is appropriate.

9) Solve for “x”.

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10) Solve for “x”.

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11) Solve for “x”.

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12) Solve for “x”.

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For the next three problems, factor each quadratic expression.

13) Factor.

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14) Factor.

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15) Factor.

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For the next four problems, solve for “x” by factoring and applying the zero product property.

16) Solve for “x”.

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17) Solve for “x”.

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18) Solve for “x”.

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19) Solve for “x”.

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In the next two problems, solve for “x” by completing the square; and then state the letter of the correct answer.

20) Solve for “x”.

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21) Solve for “x”.

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For the next two problems, write the quadratic function in vertex form as shown below. State the letter of the correct answer.

22) Write the quadratic function in vertex form.

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23) Write the quadratic function in vertex form.

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For the next two 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).

24) What is the discriminant? What is the type and number of solutions?

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25) What is the discriminant? What is the type and number of solutions?

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For the next two problems, perform the indicated operation for the complex numbers and simplify.

26) Find the difference.

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27) Find the product.

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Short Answer

28) Give an example of a quadratic function that has a maximum value. How do you know that it has a maximum value?

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29) Examine the results of the student’s work shown below. (a) What is her error? (b) What is the correct factored form?

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