Find the vertex the line of symmetry the maximum or minimum

Question

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

f(x) = - 2x²+ 2x + 5

The x-coordinate of the vertex is ___. (Type a simplified fraction.)

The y-coordinate of the vertex is ____. (Type a simplified fraction.)

The equation of the line of symmetry is x = _____. (Type a simplified fraction.)

The maximum/minimum of f(x) is _____.

The Vale of f(1/2) = 11/2 is ?

Choose the correct graph.

Question 2 If the sides of a square are lengthened by 7 cm, the area becomes 256 cm². Find the length of a side of the original square.

The length of a side of the original square is ____ cm.

Question  3 Rewrite with a rational exponent.

⁴√23 = ____. (Simplify your answer.)

Question  4

a) Solve 4x² = 20.
b) Find the x-intercepts of f(x) = 4x² - 20.

a) What are the solutions?

x = ___

(Type an exact answer, using radicals as needed. Rationalize all denominators. Express cS.s. complex numbers in terms of i. Use a comma
to separate answers as needed.)

b) What are the x-intercepts? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A. The x-intercepts are _____.

(Type an ordered pair. Type an exact answer, using radicals as needed. Rationalize all denominators. Use a comma to separate answers as needed.)

B. There are no x-intercepts.

Question 5.

Subtract the polynomials.
(- 5s²+ 9s+ 2)- (8s²+ 2) = ____ (Simplify your answer.)

Question 6.

Solve for x.

4x(x - 7) - 5x(x - 6) = - 3

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A. x = ____. (Simplify your answer. Use a comma to separate answers as needed.)

B. There is no solution.

Question 7.  If a pro basketball player has a vertical leap of about 30 inches, what is his hang time? Use the hang-time function V = 48 T².

His hang time is ___ seconds. (Simplify your answer. Type an integer or a decimal. Round to the nearest tenth.)

Question 8. Jack usually mows his lawn in 7 hours. Marilyn can mow the same yard in 4 hours. How much time would it take for them to mow the lawn together?

They could mow the lawn in ____ hours if they worked together. (Simplify your answer. Type an integer, proper fraction, or mixed number.)

Question 9. Find the greatest common factor for the group of terms.

- 30a⁴, 5a⁵

The greatest common factor is ____.

Question 10. Solve. v² - 2v- 35 = 0

Select the correct choice below and fill in any answer boxes in your choice.

A. The solution is v = ___. (Use a comma to separate answers as needed.)
B.There is no solution.

Question 11.

Simplify by removing factors of 1.

(6r² + 6r)/(42r²+ 36r)

The simplified form is ____.

Question 12. For the following equation, state the value of the discriminant and then describe the nature of the solutions.

- 14x²-8x- 10=0

What is the value of the discriminant?

Which one of the statements below is correct? 

A. The equation has two imaginary solutions.

B. The equation has two real solutions.

C. The equation has one real solution.

Question 13.

Multiply and simplify.

(25y²)/(3y2 - 24y + 48).(3y - 12)/(5y) =  ______ (Type exponential notation with positive exponents.)

Add

(2v⁴ - 2v³ + 5v²+ 13v - 11) + (v⁵ + 8v³ + 2v² - 5v + 6) + (- 5v⁴ + V²- 3v - 6)

The answer is ____. (Simplify your answer.)