# Algebra 2 Midterm

**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.

Image result for x y axis

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

73-1.jpg

**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 long division or 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.