What is the answers and break down of them,

Typing hint: Type x
2
as x^2 (shift 6 on the keyboard will give ^)
1) Solve the following quadratic equation by factoring:
a) 7 010
2
xx =++
Answers:
Show your work here:
b) Solve the quadratic equation using the quadratic formula. Read
the information in the assignment list to learn more about how to type math symbols in
MS Word, such as the square root.
0232
2
xx =−−
Answers:
Show your work here:
c) Compute the discriminant of the quadratic equation 3 .
Then write a brief sentence describing the number and type of solutions for this
equation.
Answers:
Show your work here:
2) Use the graph of y = 7 – 6x – x
2
to answer the following:a)Without solving the equation (or factoring), determine the solutions to the equation
7 – 6x – x
2
= 0 using only the graph.
Answer:
Explain how you obtain your answer(s) by looking at the graph in a brief sentence:
b)Does this function have a maximum or a minimum?
Answer:
Explain how you obtain your answer by looking at the graph in a brief sentence:
c)What are the coordinates of the vertex in (x, y) form?
Answer:
d)What is the equation of the axis of symmetry for this parabola?
Answer:
3) The profit function for the Recklus Hang gliding Service is P(x) = -0.2x
2
+ fx - m,
where f represents the set up fee for a customer’s daily excursion and m
represents the monthly hanger rental. Also, P represents the monthly profit in
dollars of the small business where x is the number of flight excursions facilitated
in that month. a) If $30 is charged for a set up fee, and the monthly hanger rental is $600; write an
equation for the profit, P, in terms of x.
Typing hint: Type x-squared as x^2
Answer:
b) How much is the profit when 40 flight excursions are sold in a month?
Answer:
Show your work here:
c) How many flight excursions must be sold in order to maximize the profit? Show
your work algebraically. Trial and error is not an appropriate method of solution –
use methods taught in class.

Answer:
Show your work here:
d) What is the maximum profit?
Answer:
Show your work here:
4) Graph the equation by completing the table and plotting the points. You may use
Excel or another web-based graphing utility.
a) y = 3x - x
2

Use the values of x provided in the table to find the y values. Show your work.
x y
-2
-1
0
1
2
3
4
5 b) Place your graph here: For help on creating your graph in Excel and inserting
graphs into a Word Doc please see the tutorial in the Assignment List.
c) Determine the two x-intercepts of this parabola in (x,y) form and explain how you
found these ordered pairs in a sentence.
Answers:

Sure, let's break down the answers to each part of the question:

1)
a) To solve the quadratic equation by factoring, we have the equation: 7x^2 + 10x + 2 = 0. We need to express this equation in factored form. Since the coefficient of x^2 is not 1, we need to factor out the common coefficient: x^2(7x + 5) + 2 = 0. Now we can set each factor equal to zero and solve for x: x^2 = 0 or 7x + 5 = 0. The first equation gives us x = 0. The second equation can be solved by subtracting 5 from both sides and then dividing by 7, giving us x = -5/7. Therefore, the solutions to the quadratic equation by factoring are x = 0 and x = -5/7.

b) To solve the quadratic equation using the quadratic formula, we have the equation: 2x^2 - 3x - 2 = 0. The quadratic formula is given by x = (-b ± √(b^2 - 4ac))/(2a). Plugging in the values a = 2, b = -3, and c = -2 into the formula, we get x = (-(-3) ± √((-3)^2 - 4(2)(-2)))/(2(2)). Simplifying further, we have x = (3 ± √(9 + 16))/4. The discriminant (b^2 - 4ac) is 41, which is positive. Therefore, we have two real solutions. Evaluating the square root, we have x = (3 ± √25)/4. This gives us x = (3 ± 5)/4, which simplifies to x = 2 or x = -1/2. Thus, the solutions to the quadratic equation using the quadratic formula are x = 2 and x = -1/2.

c) The discriminant of the quadratic equation 3x^2 is given by b^2 - 4ac. Since a = 3, b = 0, and c = 0, the discriminant is 0^2 - 4(3)(0) = 0. Since the discriminant is equal to 0, the quadratic equation has one real solution.

2)
a) Without solving the equation (or factoring), we can determine the solutions to the equation 7 - 6x - x^2 = 0 by looking at the graph. We need to find the x-intercepts, which are the points where the graph intersects the x-axis. These points represent the solutions to the equation. By looking at the graph, we can see that the x-intercepts occur at x = -1 and x = 7.

b) To determine if the function has a maximum or minimum, we can observe the shape of the graph. If the parabola opens upwards, then the function has a minimum. If the parabola opens downwards, then the function has a maximum. By looking at the graph, we can see that the parabola opens downwards, so the function has a maximum.

c) The coordinates of the vertex can be found by looking at the lowest point (maximum) or highest point (minimum) of the graph. By observing the graph, we can see that the vertex of the parabola is at the point (4, -25).

d) The equation of the axis of symmetry can be determined by finding the vertical line that passes through the vertex. Since the vertex is at (4, -25), the equation of the axis of symmetry is x = 4.

3)
a) To write the equation for the profit, P, in terms of x, we substitute the given values for f and m into the profit function. Given that f = $30 and m = $600, the profit function becomes P(x) = -0.2x^2 + 30x - 600.

b) To find the profit when 40 flight excursions are sold in a month, we plug in x = 40 into the profit function. Evaluating the function, we have P(40) = -0.2(40)^2 + 30(40) - 600. Simplifying the expression gives us P(40) = -$800.

c) To find the number of flight excursions that must be sold in order to maximize the profit, we can use the vertex formula x = -b/(2a). In this case, a = -0.2 and b = 30. Substituting these values into the formula, we have x = -30/(2(-0.2)). Simplifying further, we get x = -30/(-0.4) = 75. So, 75 flight excursions must be sold in order to maximize the profit.

d) To find the maximum profit, we substitute the value of x = 75 into the profit function P(x) = -0.2x^2 + 30x - 600. Evaluating the function gives us P(75) = -0.2(75)^2 + 30(75) - 600. Simplifying the expression gives us P(75) = $375.

4)
a) To find the y-values for the equation y = 3x - x^2, we substitute the given values of x into the equation. The table is as follows:
x | y
-2 | 10
-1 | 4
0 | 0
1 | 2
2 | 2
3 | 0
4 | -4
5 | -10

b) The graph of the equation y = 3x - x^2 can be plotted using Excel or any other graphing utility.

c) To determine the two x-intercepts of the parabola, we look for the points where the graph intersects the x-axis. From the table in part a), we can see that the x-intercepts are (-2, 0) and (4, 0). This means that when y = 0, x = -2 and x = 4.