Algebra II with Trigonometry
Benchmark Exam 2 Study Guide
Determine whether the function is linear or quadratic. Identify the quadratic, linear, and constant terms.
1. y = 3x(x – 1) + 4
2. Write the equation of the parabola in vertex form. vertex (3, 1), point (–2, 16)
3. Find a quadratic model for the set of values. (–2, 8), (0, –10), (5, 27)
4. Graph the quadratic function. State the vertex, direction of opening, x-intercepts, and y-intercept.
y = -3x² + 18x - 24
5. Graph the quadratic function. State the vertex, direction of opening, and y-intercept. y = 2(x – 3)² - 1
6. Solve by factoring. 5x² - 5x – 150 = 0
7.
Solve the equation by finding square roots. 6x² = 36
8. Solve by graphing 2x² - 12x + 10 = 0
9. Write the number in the form a + bi.
9 8
Simplify the expression.
11.
(8  i )  (2  3i )
12.
10.
(2  4i )  (3  6i )
 3   45
13.
(3i  5)(i  4)
14. Solve the quadratic equation by completing the square. x² - 6x + 10 = 0
15. Rewrite the equation in vertex form. y = x² + 8x – 1
16. Use the Quadratic Formula to solve the equation. 3x² + 2x – 7 = 0
17&18. Determine the nature of solution(s) by using the discriminant:
3x² - x + 5 = 0
9x² + 30x + 25 = 0
19. Classify –8x6 + 5x4 + 4x2 by degree and by number of terms.
20. Use a graphing calculator to determine which type of model best fits the values in the table. (Plot the points
rather than using a graphing calculator. Then look at the graph to determine the model)
x
–8
–1
0
1
8
y
8
1
0
-1
-8
21. Write 5x3 – 45x2 + 70x in factored form.
22. Write a polynomial function in standard form with zeros at 5, –2, and 3.
23. Divide 4 x  4 x  6 x  1 by
3
2
x  2 using
24. Divide by using synthetic division.
(5 x 4  x 3  3x  1)  ( x  2)
long division.
25.
26.
Find the zeros of y = x(x – 4)(x + 3). Then graph the equation.
4
2
Solve x  53x  196 .
27. Find the roots of the polynomial equation. x  7 x  13 x  3 x  18  0
4
3
2
28. Find a third-degree polynomial equation with rational coefficients that has roots –3 and 5 – i.
29.
Find all zeros of x 4  3x 3  5 x 2  12 x  4  0 .
Algebra II with Trigonometry
Benchmark Exam 2 Study Guide
Determine whether the function is linear or quadratic. Identify the quadratic, linear, and constant terms.
1. y = 3x(x – 1) + 4
2. Write the equation of the parabola in vertex form. vertex (3, 1), point (–2, 16)
3. Find a quadratic model for the set of values. (–2, 8), (0, –10), (5, 27)
4. Graph the quadratic function. State the vertex, direction of opening, x-intercepts, and y-intercept.
y = -3x² + 18x - 24
5. Graph the quadratic function. State the vertex, direction of opening, and y-intercept. y = 2(x – 3)² - 1
6. Solve by factoring. 5x² - 5x – 150 = 0
7.
Solve the equation by finding square roots. 6x² = 36
8. Solve by graphing 2x² - 12x + 10 = 0
9. Write the number in the form a + bi.
9 8
Simplify the expression.
11.
(8  i )  (2  3i )
12.
10.
(2  4i )  (3  6i )
 3   45
13.
(3i  5)(i  4)
14. Solve the quadratic equation by completing the square. x² - 6x + 10 = 0
15. Rewrite the equation in vertex form. y = x² + 8x – 1
16. Use the Quadratic Formula to solve the equation. 3x² + 2x – 7 = 0
17&18. Determine the nature of solution(s) by using the discriminant:
3x² - x + 5 = 0
9x² + 30x + 25 = 0
19. Classify –8x6 + 5x4 + 4x2 by degree and by number of terms.
20. Use a graphing calculator to determine which type of model best fits the values in the table. (Plot the points
rather than using a graphing calculator. Then look at the graph to determine the model)
x
–8
–1
0
1
8
y
8
1
0
-1
-8
21. Write 5x3 – 45x2 + 70x in factored form.
22. Write a polynomial function in standard form with zeros at 5, –2, and 3.
23. Divide 4 x  4 x  6 x  1 by
3
2
x  2 using
24. Divide by using synthetic division.
(5 x 4  x 3  3x  1)  ( x  2)
long division.
25.
26.
Find the zeros of y = x(x – 4)(x + 3). Then graph the equation.
4
2
Solve x  53x  196 .
27. Find the roots of the polynomial equation. x  7 x  13 x  3 x  18  0
4
3
2
28. Find a third-degree polynomial equation with rational coefficients that has roots –3 and 5 – i.
29.
Find all zeros of x 4  3x 3  5 x 2  12 x  4  0 .