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# 15 Problems : Graphs of Quadratic Functions - Maximum, Minimum and Vertex

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Please see the attached file for the fully formatted problems.

1. Find and label the vertex and the line of symmetry.

The vertex is _______ (type an ordered pair)
The equation of the line of symmetry is x= _________
3. Write a quadratic equation having the given number as solutions.
-4 and -1
The quadratic equation is 0= ___________
4. Give exact and approximate solutions to three decimal places.

What are the exact solutions? X= ___________
Type an exact answer, using radicals as needed. Rationalize all denominators. Express complex numbers in term of i. Use a comma to separate answers as needed. There are no approximate solutions since the solutions are integers.
6.
a) Solve.

Type an exact answer, using radicals as needed. Rationalize all denominators. Express complex numbers in term of i. Use a comma to separate answers as needed. There are no approximate solutions since the solutions are integers.
b) Find the x-intercepts of

Type an order pair. Simplify your answer. Type an exact answer, using radicals as needed. Express complex numbers in terms of i. Use a comma to separate answers as needed.
7. The number of tickets sold each day for an upcoming performance of Handel's Messiah is given by , where x is the number of days since the concert was first announced. When will daily ticket sales peak and how many tickets will be sold that day?

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

The vertex is ____________
The line of symmetry is x= _______________
The maximum/minimum value of f(x) is?
Is the value, f(-5)=-9, maximum/minimum?
9. Find the vertex, the line of symmetry, the maximum or minimum value of the quadratic function, and graph the function.

What is the vertex?

What is the equation of the line of symmetry?

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

Is the value, f(3)=-8 a minimum or a maximum?

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

The vertex is ____________

The equation of the line of symmetry is x=_____________

The maximum/minimum of f(x) is ______________
The value f(2)=8 is a minimum/maximum.

12. A student opens a mathematics book to two facing pages. The product of the page numbers is 342. Find the page numbers.

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

The vertex is _________

The line of symmetry is x= _____________

The maximum/minimum value of f(x) is ________________

Is the value, f(-6)=1, a minimum or a maximum?

14. Solve by completing the square.

15. Give exact and approximate solutions to three decimal places.

16. Find the vertex.

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

The maximum/minimum of f(x) is __________

Is the value, f(1)=3 a minimum or a maximum?

18. Give exact and approximate solutions to the three decimal places.

19.
a) Solve

b) Find the x=intercepts of

20. Find the x-intercepts and y-intercepts.

21. The width of a rectangle is 1 ft less than the length. The area is 6 ft . Find the length and the width.

22. Solve for x.

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## 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
The width is

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