Quadratic Equations – MTH133

1) Solve the following by factoring; find the solutions, factoring alone is not the objective of the problems:


Show your work here:


Show your work here:

2) If , find:

a) f(2)

Show your work here:

b) f(-3)

Show your work here:

3) Solve using the quadratic formula.

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.

Explain how you obtain your answer(s) by looking at the graph:

b) Which does this function have, a maximum or a minimum?

Explain how you obtain your answer by looking at the graph:

c) What are the coordinates of the vertex in (x, y) form?


d) What is the equation of the line of symmetry for this graph?


5) a) Calculate the value of the discriminant of .

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?


6) a) Find the corresponding y values for x= -2, -1, 0, 1, 2, 3 if .

Answer (fill in y column)
x y

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

b) How high is the rock after 1 second?
Show your work here:

c) After how many seconds will the graph reach maximum height?
Show your work here:

d) What is the maximum height?
Show your work here:

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