Write the expression in the standard form a + bi.

1) (7 + 2i)(7 - 2i)

Use factoring to find the zeros of the quadratic function.
List the x-intercepts of the graph of the function.

2) F(x) = x^{2} - x - 20

Find the zeros of the quadratic function using the Square
Root Method. List the x- intercepts of the graph of the function.

3) h(x) = (x + 5)^2 - 49

Find the zeros of the quadratic function by completing the
square. List the x-intercepts of the graph of the function .

4) f(x) = x^{2} - 12x + 27

Find the real zeros , if any, of each quadratic function
using the quadratic formula . List the x-intercepts, if any, of the

graph of the function.

5) f(x) = 7x^{2} - 19x - 6

Find the vertex and axis of symmetry of the graph of the
function.

Be exact. Using calculator is only partial credit.

6) f(x) = x^{2} + 15x - 5

**Use a graphing calculator to plot the data and find the
quadratic function of best fit.**

7) An engineer collects data showing the speed s of a given car model and its
average miles

per gallon M. Use a graphing calculator to plot the scatter diagram. What is the
quadratic

function of best fit?

Speed, s |
mph, M |

20 |
18 |

30 |
20 |

40 |
23 |

50 |
25 |

60 |
28 |

70 |
24 |

80 |
22 |

**Find the complex zeros of the quadratic function.**

8) g(x) = 3x^{2} - x + 3

Form a polynomial whose zeros and degree are given.

9) Zeros: -3, multiplicity 2; 3, multiplicity 1; degree 3

Find the x- and y-intercepts of f.

10) f(x) = -2x^{2}(x + 8)(x^{2} + 9)

Use division to find the quotient and the remainder.

11) 3x^{3} + 21x^{2} + 27x - 15 is divided by x + 5

Determine whether x - c is a factor of f(x).

12) f(x) = x^{4} + 6x^{3} + 7x^{2} + 38x - 24; x + 6

Find all the exact real zeros of the polynomial function.
Use the zeros to factor f over the real numbers .

Show the exact zero does not have a remainder.

13) f(x) = 5x^{3} - 2x^{2} + 25x - 10

**Information is given about a polynomial f(x) whose
coefficients are real numbers. Find the remaining zeros of f.**

14) Degree 5; zeros: 2, i, 2i

15) Degree 4; zeros: i, 1 + i

Find all real and complex zeros of the function and write
the polynomial as a product of linear factors.

16) f(x) = x^{3} + 4x^{2} + 8x + 8

**Answer Key**

Testname: M1111 SPRING 2009 TEST3