James Madison High School Roots of The Parabola & Polynomial Function Exam

It is very important that you show your work for this exam. You will only receive partial credit if your work is not shown.

Algebra 2 Midterm Exam
Name:
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 – 5n) + 14n.
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) = –5𝒙𝟐 – 10x + 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.
2×2+ 5x – 9 = 2x
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
𝟔𝟎𝒕
bloodstream t minutes after being taken is given by f(t) = 𝟐
.
𝒕 +𝟒𝟔
Find the amount of medicine in the blood after 20 minutes.
9. Graph f(x) = x2 + 2x – 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(5y – 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 (9𝒌𝟔 + 8𝒌𝟒 – 6𝒌𝟐 )(4𝒌𝟐 – 5).
𝟐𝒙𝟑 + 𝒙𝟐 + 𝟏
𝒙+𝟏
.
15. Find the inverse of h(x) =
𝟐𝒙 + 𝟔
𝟓
.
16. If f(x) = 2x – 1 and g(x) = 𝒙𝟐 – 2, find [g ◦ f](x).
17. Graph the function y = √𝒙 + 𝟒 – 2. Then state the domain and range of the
function.
Domain:
Range:
18. If f(x) = 3×2 – 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 Tshirt, 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.