ALGEBRA 2 10/23/14 REVIEW FOR TEST 2 (NON-CALCULATOR SECTION) What you’ll learn and why… I can learn how to solve the problems in the Practice Test so I can ace Test 2 on Monday. HW : Know the formulas and methods needed to solve each problem in the Practice Test. Warm-up: 1.Silently recite the Quadratic Formula 5x. 2.Silently recite the formula to find the x- coordinate of the vertex of a quadratic equation in standard form 5x.

The product of complex conjugates is always a real number. From this information, choices C and D should be eliminated. The answer is B 20. Your Turn: Answer Practice Test #1.

Notes: To subtract a complex number, add its opposite. Answer: C Your Turn: Answer Practice Test #2

3. Find the domain and range of each function. A D: R: B D: R: C D: R: D D: R: All real numbers Notes: The domain of a function is the set of all possible x values. The range of a function is the set of all possible y values.

3. To find the y-coordinate of the vertex, substitute the value of x into the original function. The statement which is not true is D. The vertex is at (1, 4) Your Turn: Answer Practice Test #4.

A.-7 B.-11 C. 7 D. 11 Alternative Method: You could use completing the square to convert from standard form to vertex form. Your Turn: Answer Practice Test #5

Subtract 3 from each side Divide each side by 16. Note: Eliminate answers that are not in simplest form. Choices A and B are eliminated because they have a radical in the denominator. The choices left are C and D. C has nonreal solutions while D has real solutions. Simplify.

The answer is C. Your Turn: Answer Practice Test #7.

Subtract 81 from each side. The answer is B. Your Turn: Answer Practice Test #8.

Which function has a greater negative x-intercept? A.Function A B.Function B C.The x-intercepts are equal. Solution: You need to find the negative x-intercepts of both function and then compare to find the greater number. The negative x-intercept of Function B is -1. Use factoring to find the x-intercepts of Function A. (Other methods may be used.) Look for factors of c whose sum is b. Use 5 and -1 Set each factor equal to 0. Solve for x. Your Turn: Answer Practice Test #9.

Steps: Divide each side by the GCF, 5. Subtract 12 from each side. Look for factors of -12 whose sum is 1. Use 4 and -3. Set each factor equal to 0. Solve for x. The answer is C. Your Turn: Answer Practice Test #10. Alternative Method: Work Backwards Substitute the answer choices into the given equation. See which solutions satisfy the given equation.

11. Which of the following functions has its vertex below the x-axis? Solution: To determine which vertex is below the x-axis, graph the vertex of each function. The answer is D. Is there a pattern? What pattern do you see? Given the vertex (h, k), when k < 0, then the vertex is below the x-axis. Your Turn: Answer Practice Test #11. Vertex of A: (0, 0) Vertex of B: (-4, 3) Vertex of C: (0, 2) Vertex of D: (1, -2)

12. What is the equation of the parabola shown? Notes: 1. The parabola opens up, therefore a > 0. Eliminate Choices A and B. 2. USE NICE POINTS! The point (1, 4) is on the parabola. Check by substituting x = 1 and y = 4 into the remaining equations C and D. The answer is D. Your Turn: Answer Practice Test #12.

STEPS 1. Write the original inequality. 2. Set one side of the inequality to 0. (Add 3x and 6 to each side.) 3. Combine like terms. 4. Change the inequality sign to equal sign. 5. Solve the quadratic equation to find the zeros or x-intercepts. 6. Mark the x-intercepts on a numberline. The numberline is now divided into three intervals: A, B, and C. Sketch the parabola. 7. Determine in which interval/s the solutions lie. Write the solution set using the correct inequality symbols. 8. Check by using test values. A B C

14. Which of the following quadratic equations has no real roots? Write in standard form

A.(1, 3); maximum B.(1, 3); minimum C.(3, 1); maximum D.(3, 1); minimum Notes: Since a > 0, the parabola opens up and it has a minimum value. Eliminate Choices A and C. The answer is B. Your Turn: Answer Practice Test #15.

Divide each side by -12. Simplify. Subtract 36 from each side. Substitute a = 3 and b = -6 Simplify. The answer is B.

Steps: Identify a, b, and c. Write the quadratic formula. Substitute the values of a, b, and c. Simplify. The answer is D. Alternative Method: Work Backwards

Solution: Since you are to compare the maximum value of each function, you need to find each function’s vertex. The maximum is the y-coordinate of the vertex. The answer is D.

Solution: 1. Draw x = -2, the axis of symmetry on the graph. 2. Plot the four points given in the table. 4. Connect the points to sketch the parabola. 5. Find the intervals where the x- intercepts are located. The answer is A. 3. Use symmetry to locate three other points.

HOMEWORK: Study the notes, formulas and strategies that you need to solve each problem exercise on Test 2. Remember, notes, formulas and calculators will not be allowed. This review material is posted in my.ccsd.net. Be sure to try answering all the problems here and also the ones in your Practice Test. Prepare well so you can ace this test.