# Algebra and Graphing Problems

Please see the attached file for the fully formatted problems.

Algebra problems

DIRECTIONS: It is a little trickier to do online because of the graphs. For the equations/inequalities that require a graphical solution, you will have to describe what part of your graph provides the answer. If you scan in your work, then include an actual sketch of the graph and omit the description.

EACH EXAMPLE IS WORTH 10 POINTS.

1) Solve for x using BOTH methods of algebra and graphing.

2) Solve the quadratic inequality for x. Include a graph of the parabola that is associated with this inequality ( or a description of the graph ) and write a short explanation of how the graph confirms the solution. Again, be specific in your explanation here and get at the heart of this type of inequality.

3) Solve the higher-order equation to three decimal places BY GRAPHING: .

4) Solve , using the QUADRATIC FORMULA. Convert answer(s) to three-place decimal.

5) Solve by either algebraic or graphing methods.

6) Solve by either algebraic or graphing methods.

7) Solve by completing the square.

8) Motion Under Gravity: Use the equation to determine when the height of an object is 960 feet if the initial velocity is 272 feet per second. Solve either algebraically or graphically. Include all algebra to justify response if solving algebraically. Include sketch of graph and explain how you interpreted the graph to get your answer(s).

9) Graph the function and find:

a) values of the relative maximum and minimum

b) x-intervals over which the function values are increasing and decreasing; explain what your answer means by writing in complete sentences.

10) Explain how the vertical line test determines if a graph of a set of points is a function. Make reference to the definition of function in your explanation. Do not just state what the test says but actually explain why it works!

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#### Solution Preview

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DIRECTIONS: It is a little trickier to do online because of the graphs. For the equations/inequalities that require a graphical solution, you will have to describe what part of your graph provides the answer. If you scan in your work, then include an actual sketch of the graph and omit the description.

EACH EXAMPLE IS WORTH 10 POINTS.

1) Solve for x using BOTH methods of algebra and graphing.

Solution:

1. Algebraic method

square both sides

6x-1=16

6x=16+1

6x=17

x=17/6

Make sure that 6(17/6)-1 is positive so that we could take square root.

6(17/6)-1=16.

So x=17/6 is the solution.

2. Graphing: graph y=4 and y=sqrt(6x-1) and find the point of intersection. Red line is

the graph of y=4, the blue is of y=sqrt(6x-1). The blue symbol is the intersection point.

The solution is the x-coordinate of this point

2) Solve the quadratic inequality for x. Include a graph of the parabola that is associated with this inequality ( or a description of the graph ) and write a short explanation of how the graph confirms the solution. Again, be specific in your explanation here and get at the heart of this type of inequality.

Solution: solve

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#### Solution Summary

Various graphing and algebra problems are solved. The solution is detailed and well presented.