Precalculus
2.1-2.3 Review - Krasean
Name: _____________________________
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. (f(x) = ax2 + bx + c)
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 -
3 , 0).)
If f(x) = 3x2 – 18x – 8,
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?
If 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. Write the standard (vertex) form of the quadratic function that has vertex (4,1)
and passes through the point (6, -7).
16. Write the answer to #15 in general form.
17. Find a polynomial function that has zeros of 𝑥 = 2, 4 + √5, 4 − √5.
18. Use long division (it’s the only way) to find the quotient of
(5x3 – 2x2 + 4x – 9) ÷ (x2 + 5).
19. Use synthetic division to find (4x3 – 5x – 8) ÷ (x + 6). Remember to use 0x2!
20. What are the possible rational zeroes of the function 7x3 + 3x2 + x – 8? Don’t do any
actual division, just list the possible answers.
21. Use synthetic division to find f(3) if f(x) = 5x4 – 2x2 + 2x – 7. Remember to use 0x3!
22. Is (x + 7) a factor of 3x3 +3x2 – 11x + 21? Use synthetic division and the remainder
theorem.