Download Chapter 4 Test Review

Name:________________________________________Date:___________________________Period:_______
Algebra 2
Chapter 4 Test Review
Quadratic Functions
Sections that are covered in this test:
o Sections 4-1/4-2: Parabola’s-graphing, translating, etc (both standard and vertex form)
o Section 4-4: Factoring quadratic expressions
o Section 4-5: Solving Quadratic Equations by factoring
o Section 4-6: Solving Quadratic Equations by completing the square
o Section 4-7: Solving Quadratic Equations using the Quadratic Formula and Discriminant
How to Solve Quadratic Equations by Factoring:
1. The equation must equal zero.
2. Factor the polynomial.

Look for GCF and factor it out, if applicable.

Look to see if the polynomial is a binomial or trinomial.
o If binomial, is it a Difference of Two Squares?
o If Trinomial, use F/S method.

If it is a Perfect Square Trinomial, write the answer as a binomial squared.
3. Set each variable expression equal to zero and solve for the variable(s).
Solve each quadratic equation by factoring.
1. 4 x 2  4 x  1
2. g 2  49
3. x 2  25 x  0
4. 3a 3  30a 2  63a
How to Solve Quadratic Equations by Completing the Square:
1. Rewrite the equation in the form
.
2. Make sure a  1 !
* May need to divide each term in the equation by the coefficient of
3. Complete the square by adding
.
to both sides of the equation.
4. Factor the perfect square trinomial.
5. Take the square root of each side of the equation.
6. Solve for x.
Solve each quadratic equation by completing the square.
5. 3x 2  24 x  9  0
6. x 2  5 x  3 x  11
7. x 2  12 x  35
8. 2 x 2  12 x  2  0
How to Solve Quadratic Equations by the Quadratic Formula:
1. The equation must equal zero.
2. Identify a, b, c values.
3. Plug those values into the Quadratic Formula.
4. Simplify to solve for x.
Formula:
Solve using the Quadratic Formula. Write answers as integers, fractions, or in simplest radical form.
9. x 2  10 x  22  0
10. x 2  16  8 x
11. 3 x 2  5 x  2
12. 4 x 2  x  3
How to find the discriminant:
1. Use b 2  4ac
2. positive number = 2 solutions, zero = 1 solution, negative number = 0 solutions
Find the discriminant and determine the number of solutions.
13. 3 x 2  8 x  3
14. 2 x 2  8 x  8
Discriminant _____________
Discriminant _____________
# of solutions_____________
# of solutions_____________
15.  x  7 x 2  4
16. 2 x  x 2  x
Discriminant _____________
Discriminant _____________
# of solutions_____________
# of solutions_____________
Give the specified information and Graph the parabola on the coordinate plane provided.
17. y  2 x 2  8x  2
Vertex: ___________________
Axis of Symmetry: ________________
y-intercept: ________________
Opens up/down? ___________
Max/Min value? ____________
Domain: __________________
Range: __________________
18. y  x 2  2 x  3
Vertex: ___________________
Axis of Symmetry: ________________
y-intercept: ________________
Opens up/down? ___________
Max/Min value? ____________
Domain: __________________
Range: __________________
Give the specified information and Graph the parabola on the coordinate plane provided. Describe the
transformation of from the parent graph of y  x 2 .
19. y 
1
x  42  2
2
Vertex: ___________________
Axis of Symmetry: ________________
y-intercept: ________________
Opens up/down? ___________
Max/Min value? ____________
Domain: __________________
Range: __________________
Transformation: ______________________________________________________________________
______________________________________________________________________
20. y  4 x  3  1
2
Vertex: ___________________
Axis of Symmetry: ________________
y-intercept: ________________
Opens up/down? ___________
Max/Min value? ____________
Domain: __________________
Range: __________________
Transformation: ______________________________________________________________________
______________________________________________________________________