3.8.4 Test (TST): Quadratic Equations and Functions
Answer the following questions using what you've learned from this unit. Write your answers in the space provided. Be sure to show all work.
Graph the parabola. Use the key features of the graph that you identified in Part d. (3 points)
In this problem, only positive values of x make sense. Why? (1 point)
What point on your graph shows a total area that includes the pool but not the pool deck? (1 point)
The community decided on a pool area that adds 6 yards of pool deck to both the length and the width of the pool. What is the total area of the pool and deck when x = 6 yards? (2 points)
Step 1: Write an equation for the area of the enclosed space in the form y = (side length)2. Hint: Don't forget to add x to each side of the hot tub. (1 point)
Step 2: Substitute the area of the enclosed space for y in your equation. (1 point)
Step 3: Solve your equation from Part b for x. (3 points)
Step 4: What is the width of the deck around the hot tub? Hint: One of the answers from Part c is not reasonable. (1 point)
Comparing Quadratic Functions
4. Two different quadratic functions have graphs with the same vertex. Which function's graph increases faster between x = 2 and x = 3?
Function A
Function B
x
y
–1
12.5
0
5
1
0.5
2
–1
3
0.5
4
5
5
12.5
a. What is the vertex of each function's graph? (1 point)
b. What is the average rate of change in function A between x = 2 and x = 3? (2 points)
c. What is the average rate of change in function B between x = 2 and x = 3? (2 points)
d. Which function's graph increases faster between x = 2 and x = 3? (1 point)
Solving Systems of Quadratic Equations
5. Solve this nonlinear system of equations. Show your work.
y = –x2 + 6x – 5
y = 3
a. Use substitution to combine equations. Rewrite so that one side is equal to 0. (1 point)
b. Factor your equation from Part a. (1 point)
c. Identify the x-values of the solutions. (1 point)
d. Identify the solutions to the system. (1 point)
