# Quadratic Equations

MTH133

Unit 2 Individual Project

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:

Show your work here:

d) What is the maximum height?

Answer:

Show your work here:

https://brainmass.com/math/basic-algebra/229670

#### Solution Summary

This solution includes detailed explanations to all the problems.