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Quadratic Function Homework

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) = x2 - 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) = x2 - 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) = 7x2 - 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) = x2 + 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) = 3x2 - 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) = -2x2(x + 8)(x2 + 9)

Use division to find the quotient and the remainder.
11) 3x3 + 21x2 + 27x - 15 is divided by x + 5

Determine whether x - c is a factor of f(x).
12) f(x) = x4 + 6x3 + 7x2 + 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) = 5x3 - 2x2 + 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) = x3 + 4x2 + 8x + 8

Answer Key
Testname: M1111 SPRING 2009 TEST3

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