# 20 Problems : Graphs, Quadratic Equations and Word Problems

Please see the attached file for the fully formatted problems.

1. Find the vertex, the line of symmetry, the maximum or minimum value of the quadratic function, and graph the function.

F(x) =

The vertex is ?

Type an ordered pair.

The line of symmetry is

2. Solve

(b) Find the x-intercepts of f(x) =

3. Find the vertex, the line of symmetry, the maximum or minimum value of the quadratic function, and graph the function on paper.

f(x) = . What is the vertex? Type an ordered pair.

(b) What is the equation of the line of symmetry?

(c) What is the maximum/minimum of f(x)?

(d) Is the value, f(4) =-21 a minimum or a maximum?

4. Find and label the vertex and the line of symmetry. Graph the function.

The vertex is? Type and order pair

(b) The equation of the line of symmetry is x=

5. Determine the nature of the solutions of the equation.

6. Find the vertex, the line of symmetry, and the maximum or minimum value of f(x). Graph the function

The vertex is

Type an ordered pair.

(b) What is the maximum/minimum value of f(x)?

(c) Is the value, f(-7) =1, a minimum or maximum?

7. Solve the formula for the given variable. Assume all variable represent nonnegative numbers

, for s

8. The length of a rectangle is twice the width. The area is . Find the length and the width

The length is

Simplify your answer

The width is

Simplify your answer

9. Solve by completing the square.

Type N if there is no solution

10. Solve for X

Type N if there is no solution

11. A farmer decides to enclose a rectangular garden, using the side of a barn as one side of the rectangle. What is the maximum area that the farmer can enclose with 80 ft of fence? What should the dimension of the garden be to give this area?

The maximum area that the farmer can enclose with 80 ft of fence is ....sq ft.

The dimension of the garden to give this area is 40 ft by..ft.

12. Give exact and appropriate solutions to three decimal places.

13. Write a quadratic equation in the variable x having the given numbers as solutions. Type the equation in standard form,

The solutions are, -9, 1

The equation is

14. Give exact and appropriate solutions to three decimal places.

15. Find the x-intercepts and y-intercepts for f(x)

The x-intercepts is/are

The y-intercepts is/are

Type an ordered pair. Type an integer or a decimal. Round to the nearest tenth. Use commas to separate answers as needed. Type N if there is no intercept.

16. Determine the nature of the solutions of the equation.

Does the equation has two real solutions

Does the equation has a two non-real solutions

Does the equation has on real solution

17. Find the vertex, the line of symmetry, the maximum or minimum value of the quadratic function, and graph the function.

(a) What is the vertex? Type and ordered pair.

(b) What is the equation of the line of symmetry?

(c) What is the maximum/minimum of f(x)?

(d) Is the value, f(2) =-3 a minimum or a maximum?

18. Solve

Type an exact answer, using radicals as needed. Rationalize all denominators. Express complex numbers in term 1. Use a comma to separate answer as needed.

(b) Find the x-intercepts of f(x) =

Type as ordered pair. Type an exact answer, using radicals as needed. Rationalize all denominators. Express complex numbers in terms of 1. Use a comma to separate answers as needed. Type N if there are no x-intercepts.

19. A student opens a mathematics book to two facing pages. The product of the page number is 2352. Find the page numbers.

The first page is

The second page is

20. Give exact and appropriate solutions to three decimal places.

The exact solutions are

Use radicals as needed. Use a comma to separate answers.

The appropriate solutions to 3 decimal places are