Precalculus
Worksheet 2.1-2.2 Review (Rev 2)
Name: _____________________________
Date: ________________Hour: _________
Given the function f(x) = -2(x – 4)2 + 14
1. What are the coordinates of the parabola’s vertex?
2. Does the parabola open up or down?
3. Does the parabola have a minimum or a maximum?
4. Set f(x) = 0 (or y = 0) and algebraically find the EXACT locations of the x-intercepts.
[you should have some radical signs in your answer]
5. Write the function in general form. (ie. f(x) = ax2 + bx + c)
6-8. Given the function f(x) = x2 – 14x + 46
6. What is the location of the y-intercept?
7. The function is in general form. Put it into standard form by completing the square.
If you did the above correctly, you should see that the vertex is at (7, -3)
8. Now take your answer to #7, set it equal to zero, and find the locations of the
x-intercepts (like you did in #4). Show your work.
(The answers should be (7 + 3 , 0) and (7 9-10. Given f(x) = 3x2 – 18x – 8,
3 , 0).)
9. Write the function in standard form [Remember to first factor out “a” from the first
two terms before completing the square]
10. What are the coordinates of the vertex?
11-14. Given the function (written in factored form for your convenience)
f(x) = (x + 2)(x +2)( x + 1)(x + 1)(x + 1)( x – 5)(x – 5)
11. What are the zeros and the multiplicity of each?
12. What is the degree of this function?
13. Describe the “end behavior” [i.e. rises to the left, rises to the right – this isn’t the
answer by the way].
14. Sketch (roughly) a graph of what this might look like. Show the x-intercepts and yintercept.
15-16. Write the standard (vertex) form of the quadratic function that has vertex
(4,1) passes through point (6, -7).
16. Write the answer to #15 in general form.
17. Find a polynomial function that has zeros x = 2, 4 +√5, and 4 - √5
18. Use a graphing calculator to approximate to the nearest thousandth any real zeros
and relative extrema for f(x) = -3x3 – 4x2 + x – 3 .