Name
Date
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Quadratic Practice #4
On a separate sheet of paper -
in order and organized Try EVERY problem.
SHOW WORK!!!!!
A. Quadratic Formula: Use the quadratic formula to find the x-intercepts of each function.
1. y = 4x2 + 16x -2
2. y = x2 + 12x + 1
3. y = -2x2 – 12x – 4
4. y = 10x2 + 2x + 3
5. y = x2 + 6x + 10
6. y = 4x2 – 56x + 202
B. Graphing verification: Graph each function from Part A on your graphing calculator. Using the
calculate menu {2: ZERO}, verify that your algebra is correct.
C. Vertex from standard form: Using x = -b/(2a) and substitution, find the vertex of each function
in part A.
D. Finding the vertex: Given a function in y = ax2 + bx + c form, state three ways you could find the
vertex. Which method do you prefer? Why?
E. Finding x-intercepts: Given a function in x2 + bx + c form, state three ways you could find the xintercepts of the function. Which method do you prefer? Why? Does your choice change if the
function is in y = ax2 + bx + c form?
F. Applying the skills: (hint – always draw a picture of the situation!)
1. A documentary film crew is making a new film about frogs. They are hoping to achieve the same
acclaim as the makers of March of the Penguins. During filming, a frog jumps from one lily-pad to
another. The path of the jump can be modeled by the function h = -t2 + 16t – 60. {h = the frog’s
height above the pond in inches, t = the time in seconds after a documentary crew begins filming
the frog.} Using ALGEBRA, answer the following questions (answer in full sentences referring to
specifics of the situation):
a. What is the greatest height the frog reaches in this jump?
b. When did the from reach this height?
c. Use a second algebraic method to verify your answer to questions a and b.
d. When did the frog leave the first lily-pad?
e. When did the frog and on the second lily-pad?
f. Use a second algebraic method to verify your results in question d and e.
g. How many seconds did the frog’s jump last?
2. A fountain shoots water eastward out of a spigot (water spout) located on the side of a building.
The water reaches a height of 10 feet when the water is 6 feet from the side of the building. 14 feet
from the building, the water hits the ground. Using ALGEBRA, do/answer the following:
a. Write a function for this situation. Use h to represent the height of the water and d to
represent the distance from the building.
b. How high is the spigot on the building? (hint: what is the value of d?)
c. If the fountain designer wanted the water to start inside the building, from a floor level
spigot, how far inside the building would the spigot need to be located? (Assume a hole will
be cut in the wall for the water to go through!)
G. Interpreting Word Problems
1. In what kinds of situations would you write a vertex form equation? (What information would
the problem give you?)
2. In what kinds of situation would you convert a given equation to vertex form?
3. In what kinds of situations would you write a factored form equation? (What information would
the problem give you?)
4. In what kinds of situation would you convert a given equation to factored form?
5. Review questions 2 and 4. What other methods could you use to find the vertex or x-intercepts
of a function if you did not want to convert the equations?
6. Suppose the filmmakers from question F1 above film a second frog’s jump. When asked the
greatest height of the frog, an mathematical assistant says “(7, 15)” because he figured out that
point is the vertex of the frog’s path. Explain why this is not a good answer. Using the information
from the assistant, write what his response should have been.
7. Our assistant, who’s having a rough day, is asked to state when the frog left the first lily-pad, he
says “(12,0) and (2, 0).” Help him rephrase his answer to address the actual question.