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
