ALG2 James Madison High School Pythagorean Theorem Questions Response

Algebra 2 worksheet with functions, graphing, linear equations. Also solving inequalities and graphing.

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 bloodstream t minutes
𝟔𝟎𝒕
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 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.