Quadratic Equations – MTH133
1) Solve the following by factoring; find the solutions, factoring alone is not the objective of the problems:
a)
Answer:
Show your work here:
b)
Answer:
Show your work here:
2) If , find:
a) f(2)
Answer:
Show your work here:
b) f(-3)
Answer:
Show your work here:
3) Solve using the quadratic formula.
Answer:
Show your work here:
4) Use the graph of to answer the following:
a) Without solving the equation, or factoring, determine the solution(s) to the equation using only the graph.
Answer:
Explain how you obtain your answer(s) by looking at the graph:
b) Which does this function have, a maximum or a minimum?
Answer:
Explain how you obtain your answer by looking at the graph:
c) What are the coordinates of the vertex in (x, y) form?
Answer:
d) What is the equation of the line of symmetry for this graph?
Answer:
5) a) Calculate the value of the discriminant of .
Answer:
Show your work here:
b) By examining the sign of the discriminant in part a, how many x-intercepts would the graph of have? Why?
Answer:
6) a) Find the corresponding y values for x= -2, -1, 0, 1, 2, 3 if .
Answer (fill in y column)
x y
-2
-1
0
1
2
3
Show your work here: (type x-squared as x^2 unless using a superscript feature).
b) Use Microsoft Excel or another web-based graphing utility to plot the points found in part a and to sketch the graph. Read the information in the assignments list to learn more about how to graph in MS Excel.
7) The path of a falling object is given by the function where represents the initial velocity in ft/sec and represents the initial height in feet.
a) If a rock is thrown upward with an initial velocity of 64 feet per second from the top of a 25-foot building, write the height (s) equation using this information.
Typing hint: Type t-squared as t^2
Answer:
b) How high is the rock after 1 second?
Answer:
Show your work here:
c) After how many seconds will the graph reach maximum height?
Answer:
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d) What is the maximum height?
Answer:
Show your work here:
