# college Algebra

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1) Solve the following by factoring:

a)

b)

2) If , find

a) f(2)

b) f(-1)

3) Solve 6x2 + 3x – 18 = 0 using the quadratic formula.

4) Use the graph of y = x2 + 4x - 5 to answer the following:

a) Without solving the equation or factoring, determine the solution(s) to the equation, , using only the graph.

b) Does this function have a maximum or a minimum?

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 .

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 = -4, -3, -2, -1, 0, 1, 2 if .

x y
- 4
- 3
- 2
- 1
0
1
2

Show your work here: (type x-squared as x^2 unless using a superscript feature).

b) Use Microsoft Excel to plot the points found in part a and to sketch the graph.

Graph:

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. The variable t is time in seconds, and s is the height of the object in feet.

a) If a rock is thrown upward with an initial velocity of 32 feet per second from the top of a 40-foot building, write the height equation using this information.

Typing hint: Type t-squared as t^2.

b) How high is the rock after 0.5 seconds? Show all work.

c) After how many seconds will the rock reach maximum height? Show all work.

d) What is the maximum height? Show all work.

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