# Solving Equations and Word Problems

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1.

2. Winston can mow his dad's lawn in 1 hour less than it takes his brother Willie. If they take 2 hours to mow it when working together, then how long would it take Winston working alone?

3. Solve equation for x

4. Find all real and imaginary roots of

5. Compute value of the discriminant and give the number of real solutions to the quadratic equation

Discriminant:

Real Solutions:

6. Solve

7. When a ball is thrown, its height in feet after seconds is given by the equation

,

where is the initial upwards velocity in feet per second. If feet per second, find all values of for which feet. Do not round any intermediate steps. Round your answer to decimal places.

8. graph the solution to the quadratic inequality

.

9. Graph the parabola. Need the vertex and four points.

10. Graph the parabola. Need the vertex and four points.

11. Graph the parabola. Need the vertex and four points

12. Graph the inequality. Need the vertex and four points

13. The function h is defined by the following

H(x) = 4x+2

Complete

X H(x)

-4

-3

0

2

3

14. The function f is defined by the following function table. Graph the function.

X f(x)

-3 1

0 0

1 0

3 3

4 -1

15. Solve the following equation for x by using the quadratic formula.

16. Compute value of the discriminant and give the number of real solutions to the quadratic equation

Discriminant

Number of real numbers

17. Graph the domain of function g defined by

18. Find the x-intercept(s) and the coordinates of the vertex for the parabola

19. Find the roots of the quadratic equation

20.Solve where u is a real number. Simplify as much as possible.

21. Graph equation

22. Write the sets using interval notation

a. , where

b.

23. Graph set on a line.

24. Solve where u is a real number. Simplify answer as much as possible.

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1.

Let

When u = 3,

When u = 6,

Solutions:

2. Winston can mow his dad's lawn in 1 hour less than it takes his brother Willie. If they take 2 hours to mow it when working together, then how long would it take Winston working alone?

Winston working alone: x hours

Then Willie working alone: (x +1) hours.

Assume the lawn is A square feet.

The speed of Winston is . The speed of Willie is .

When working together, the rate at which they are working is . So it takes them hours to finish the lawn.

So

Then multiplying (2x + 1) to both sides of equation:

Discard the negative result.

Then it takes hours or about 3.56 hours to finish the lawn when Winston working alone.

3. Solve equation for x

Simplify the equation

4. Find all real and imaginary roots of

5. Compute value of the discriminant and give the number of real solutions to the quadratic equation

Discriminant:

Real Solutions: two repeated roots, or say 1 solution since the discriminant is 0.

6. Solve

7. When a ...

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