Reply

1. Solve for x: 2x² = -11x-15 (Type an integer or simplified fraction)

 

2. a. Find the vertex (Type an ordered pair). b. Find the line of symmetry. c. Find the maximum or minimum value of f(x): f(x) = -(x+1)² -8

d. Is the value of f(-1)=-8 minimum or maximum?

 

3. Solve for c: (assume all variables represent non-negative numbers) E=kc²

 

4. Give exact and approximate solutions to three decimal places. x²-7x+7=0

a. exact solutions are? (use radicals as needed) b. approximate solutions are?

 

5. a. Solve 5x²=10 What are the solutions (type an exact answer using radicals as needed, rationalize all denominators, and express complex numbers in terms of i)

b. Find the x-intercepts of f(x)=5x²-10 (type an ordered pair, rationalize denom. etc)

 

6. Do the following solutions to the equation have two non-real solutions, one real solution, or two real solutions? x²-x+5=0

 

7. Determine the nature of the solutions (2 imaginary solutions, 2 real solutions, or 1 real solution) x²-11=0

 

8. Solve by completing the square: x² + 5/2 x = 5 (type a simplified fraction, use radicals as needed, express complex numbers in terms of i)

 

9. Find the vertex, line of symmetry, and the maximum or minimum value of the quadratic function. f(x)=4x²-16x+17

 

10. a. Solve 3x+x(x-1)=0 (What are the solutions)

b. What are the x intercepts? f(x)=3x+x(x-1)

 

11. (x-9)²=12 a. What are the exact solutions

b. What are the approximate solutions (rounded to three decimal places)

 

12. Write a quadratic equation in the variable x having the given numbers as solutions. Type the equation in standard form, ax²+bx+c=0

The solutions are -7,4

 

13. y²-16y+64=81 a. What are the exact solutions

 

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

f(x)=x²-6x+2 (type an ordered pair, integer or decimal, round to tenth) type N if no intercept.

 

15. Suppose you are an event coordinator for a large theater. One of the hottest broadway musicals has started to tour, and your city is the first stop on the tour. You need to supply info about projected ticket sales to the box office manager. The manager uses this information to anticipate staffing needs until the tickets sell out. You provide the manager with a quadratic equation that models the expected number of ticket sales for each day x. (x-1 is the day tickets go on sale)

Tickets = -0.2x²+12x+11

a. Does the graph of this equation open up or down? How did you determine this?

b. Describe what happens to ticket sales as time passes.

c. Use the quadratic equation to determine the last day tickets will be sold.(Note: write your answer in terms of the number of days after ticket sales begin)

d. Will tickets peak or be at a low during the middle of the sale? How do you know?

e. After how many days will the peak or low occur?

f. How many tickets will be sold on the day when the peak or low occurs?

g. What is the point of the vertex? How does this number relate to answers in parts e and f?

h. How many solutions are there to the equation -0.2x²+12x+11=0? How do you know?

i. What do the solutions represent? Is there a solution that does not make sense? If so, in what ways does the solution not make sense?

 

Thank you!!