James Madison High School Algebra 2 Algebraic Equations Exercise Exam Practice.

### Question Description

*Directions: *Use what you have learned in this course to answer the following questions. Justify your responses completely. Each question is worth 5 points.

1. Solve for *n*: –6(*n *– 8) = 4(12 – 5*n*) + 14*n*.

2. For f(*x*) = 2|*x*+3| – 5, name the type of function and describe each of the three transformations from the parent function f(*x*) = |*x*|.

3. Determine whether *f*(*x*) = –5 – 10*x *+ 6 has a maximum or a minimum value. Find that value and explain how you know.

4. The median weekly earnings for American workers in 1990 was $412 and in 1999 it was $549. Calculate the average rate of change between 1990 and 1999.

5. Find the roots of the parabola given by the following equation. 2*x*2+ 5*x *– 9 = 2*x*

6. Describe the end behavior and determine whether the graph represents an odd-degree or an even-degree polynomial function. Then state the number of real zeros.

7. GEOMETRY Recall the formula for finding the area of a rectangle. Define a variable for the width and set up an equation to find the dimensions of a rectangle that has an area 144 square inches, given that the length is 10 inches longer than its width.

DIMENSIONS:

Length: Width:

8. The amount *f*(*t*) of a certain medicine, in milligrams, in a patient’s bloodstream *t *minutes after being taken is given by *f*(*t*) = .

Find the amount of medicine in the blood after 20 minutes.

9. Graph f(*x*) = *x*2 + 2*x *– 3, label the function’s x-intercepts, *y*-intercept and vertex with their coordinates. Also draw in and label the axis of symmetry.

+

10. Determine whether the relation shown is a function. Explain how you know.

11. Solve the inequality and graph the solution on a number line. –3(5*y *– 4) ≥ 17

12. Assume that the wooden triangle shown is a right triangle.

a. Write an equation using the Pythagorean Theorem and the measurements provided in the diagram.

Hint: (leg 1)2 + (leg 2)2 = (hypotenuse)2

b. Transform each side of the equation to determine if it is an identity.

13. Use synthetic division to find the quotient of

+ + . +

14. Simplify (9 + 8 – 6 )(4 – 5).

15. Find the inverse of h(*x*) = + .

16. If f(*x*) = 2*x *– 1 and g(*x*) = – 2, find [g ◦ f](*x*).

17. Graph the function *y *= √ + – 2. Then state the domain and range of the function.

Domain:

Range:

18. If f(*x*) = 3*x*2 – 2 and g(*x*) = 4x + 2, what is the value of (f + g)( 2) ?

The price of a sweatshirt at a local shop is twice the price of a pair of shorts. The price of a T-shirt at the shop is $4 less than the price of a pair of shorts. Brad purchased 3 sweatshirts, 2 pairs of shorts, and 5 T-shirts for a total cost of $136.

19. Let *w *represent the price of one sweatshirt, *t *represent the price of one T- shirt, and *h *represent the price of one pair of shorts. Write a system of three equations that represents the prices of the clothing.

20. Solve the system. Find the cost of each item.

James Madison High School Algebra 2 Algebraic Equations Exercise Exam Practice