Pre-Calculus
Test Review
Name:
Chapter 2: 1-5
Date:
What you need to be able to do:
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1.
2.
Identify all key characteristics of a quadratic function
(domain, range, vertex, axis of symmetry, x-intercepts, y-intercepts)
Rewrite a quadratic function into vertex form.
(complete the square)
Write the function for a quadratic with given conditions
State the end behavior in limit notation
Write the function for a polynomial with given conditions
Sketch a polynomial function using end behavior and zeros.
Long division
Synthetic division
Listing all possible rational zeros
Write a polynomial function as a product of linear factors
Use the remainder theorem to evaluate a polynomial function
Multiply complex numbers and simplify complex numbers
2. Given
a. vertex
b. Axis of Symmetry
c. Domain
d. x-intercepts
e. Range
f. y-intercept
2. Given
a. vertex
b. Axis of Symmetry
c. Domain
d. x-intercepts
e. Range
f. y-intercept
3. Give the standard (vertex) form of the function
a.
b.
c.
4. State the end behavior in limit notation
a.
b.
c.
d.
5. Use long division to divide:
a.
b.
6. Use synthetic division to divide. Write the answer in polynomial form.
a.
b.
c.
5. Use synthetic division to show that
is a factor of
6. Write the polynomial function
as the product of linear factors.
7. Find all the zeros of
given one of it’s factors:
8. List all the possible rational zeros of the function
9. Find a polynomial function with integer coefficients
that has zeros of
and degree 3
10. Find a polynomial function with integer coefficients
That has zeros of
11. Find a polynomial function with integer coefficients
With zeros
and whose right side goes down.
12. Simplify the following:
a.
b.
c.
d.
e.
f.
g.
h.
i.
j.
13. Find a polynomial function that has integer coefficients
With zeros
14. Find a polynomial function that has integer coefficients
With zeros
15. Use the given zero to find all the zeros of the function
16. Find a quadratic function that has a vertex of
And goes through the point
17. Find a quadratic function that has a vertex of
And goes through the point
18. Find two quadratic functions, one that opens up and one that
Opens down which goes through the points