Quadratic equations Questions and Answers

The global spending on travel and tourism (in billions of dollars) can be described by the equation y = 1.48x²- 25.23x + 416.91 where x equals the number of years past 1990.+ Find the year after 1990 in which spending is projected to reach $1,968 billion. (Round your answer to the nearest year.)

Using data from 2002 and with projections to 2024, total annual expenditures for national health care (in billions of dollars) can be described by E = 4.61x² + 43.4x + 1620 where x is the number of years past 2000.+ If the pattern indicated by the model remains valid, in what year does the model predict these expenditures will reach $7,071 billion?

List the roots of the parabola: y = 4x² + 8x - 2 In other words, list the solutions of the equation: 0 = 4x² + 8x - 2 Your answers must be in exact form, do not give their decimal values. Separate multiple roots with a comma.

The temperature T, in degrees Fahrenheit, of a person during an illness is given by the function T(t) = 6t/t^2+1+98.6, where t= time, in hours. Find the interval over which the temperature was over 100⁰.

(a) Find the vertex and axis of symmetry of the quadratic function. (b) Determine whether the graph is concave up or concave down. (c) Graph the quadratic function. f(x) = (x - 1)² - 4 (a) The vertex is (). (Type an ordered pair.) The axis of symmetry is. (Type an equation.)

Solve the following quadratic inequality. x2+5x+4≥0 Submit your answer by dragging the movable blue points on the number line. For an interval that extends to +∞ or -∞o move the blue points to the right or left end of the number line (shown as a dashed line). You can select whether each endpoint of your chosen interval(s) is open or closed by sliding the respective orange switches up or down. Note that the blue line segment above the number line indicates the interval(s) you have chosen and whether the endpoints are open or closed.

An object is thrown upward at a speed of 131 feet per second by a machine from a height of 14 feet off the ground. The height of the object after t seconds can be found using the equation h(t) = 16t2 + 131t+ 14. Give all numerical answers to 2 decimal places. When will the height be 53 feet? At units: When will the object reach the ground? units: When will the object reach its maximum height? units: What is its maximum height? units:

Solve the following quadratic inequality. x²-x-6≤0 Submit your answer by dragging the movable blue points on the number line. For an interval that extends to +∞ or -∞o move the blue points to the right or left end of the number line (shown as a dashed line). You can select whether each endpoint of your chosen interval is open or closed by sliding the respective orange switches up or down. Note that the blue line segment above the number line indicates the interval you have chosen and whether the endpoints are open or closed.

Given f(x) = x² + 6x +16, what is the y- intercept? A y = 20 By=16 Cy=1 Dy=0

Abigail has $30.00 to buy groceries. She needs to buy some apples, some bananas, and 3 pounds of potatoes. Fuji apples are $1.79 a pound, bananas are $0.36 each, and potatoes are $2.99 for a 3 lb. bag. If a represents the number of pounds of apples Abigail buys and b represents the number of bananas she buys, which expression represents the amount of change she receives after her purchases? 30.00-a-b 1.79a +0.36b+ 2.99 30.00-(1.79a +0.36b+ 2.99) 30.00+ (1.79a + 0.36b+ 2.99)

A quadratic function f(x) is hidden from view. You must find all intervals where f(x) is increasing. Choose the form of the quadratic function f(x) that you would like to see in order to answer the question most efficiently.

Which of the following polynomial equations are equivalent? Select all that apply. I.ab(x − 3)(x + 3) = abx² - 6abx - 9ab II.(-x+3)² - 3x² + 2 = -(2x² - 6x - 11) III.(2x-4)² - 2x = 2(2x² - 9x + 8)

Use the Intermediate Value Theorem to determine whether the polynomial function has a real zero between the given integers. f(x) = 8x² + 2x³+ 9x - 9; between -2 and -1

Solve for x in x2 + 5x-6 = 0 using the Quadratic Formula. x = 5,6 x = 2,3 x=1, -6 x = -2, -3 x = -1, -6

Franco borrows a total of $5,000 in student loan from two lenders. One charges 4.1% simple interest and the other charges 6.1% simple interest. He is not required to pay off the principal for 3 yr. However, at the end of 3 yr, he will owe a total of $825.00 for interest from both loans. How much did he borrow from each lender? Select one: a. She borrowed $1,100 at 4.1% and $3,900 at 6.1%. b. She borrowed $3,900 at 4.1% and $1,100 at 6.1%. c. She borrowed $1,500 at 4.1% and $3,500 at 6.1%. d. She borrowed $3,500 at 4.1% and $1,500 at 6.1%.

Consider the following equation 28x²+28x + 7 = 0. (a) Solve the equation by completing the square. NOTE: Enter your solutions exactly. If there is only one solution, enter it twice. (b) Solve the equation using the quadratic formula and give the values for b and e given that a =28. NOTE: Enter your solutions exactly. If there is only one solution, enter it twice.

Without solving, say whether the equation (x + 4)² = 19 has two solutions, one solution, or no solution. The equation has because

Given a polynomial that has zeros of -1, 7i, and -7i and has a value of 1000 when x = 1. Write the polynomial in standard form ax + bxn-1+. Answer using reduced fractions when necessary. ....

Factor the following expression completely: r² -10r + 25

Factor the following expression completely: x + 12x + 27

Factor the following expression completely: 27x² +24x16

Solve the equation: m2 - 6m = 0

Decide whether the following statement is true or false. The graph of f(x) = 4x² + 5x - 7 opens up. Choose the correct answer below. False True

Here is a quadratic function in factored form. Fill in the blanks about the vertex and intercepts. Enter intercepts as ordered pairs, aka points. Then graph the quadratic y = -3(z − 1)(z + 1) Vertex = y-intercept = I-intercepts=

The area (in square inches) of a rectangle is given by the polynomial function A(y) = y² + 5y + 6. If the length of the rectangle is (y + 2) inches, what is the width?

3. Evin is walking home from the museum. She starts 38 blocks from home and walks 2 blocks each minute. Evin's distance from home is a function of the number of minutes she has been walking. (a) Which variable is independent and which variable is dependent in this scenario? (b) Fill in the table below for a variety of time values. Time, 1, in minutes Distance from home, D, in blocks (c) Determine an equation relating the distance, D, that Evin is from home as a function of the number of minutes, 1, that she has been walking. 0 1 5 10 (d) Determine the number of minutes, t, that it takes for Evin to reach home.

Use z scores to compare the given values. The tallest living man at one time had a height of 240 cm. The shortest living man at that time had a height of 65.6 cm Heights of men at that time had a mean of 171.12 cm and a standard deviation of 7.39 cm. Which of these two men had the height that was more extreme? Since the z score for the tallest man is z= and the z score for the shortest man is z= man had the height that was more extreme. (Round to two decimal places) the

Solve the equation. List both the exact solution and its approximation rounded to two decimal places. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) 12x²136x + 285 = 0 Exact solution: x = Approximate solution: x =

ks. Diagrams are not to scale unless otherwise stated. 2. The coordinates of the endpoints of ABC are A(-8,-2) and C(16,6). What are the coordinates of point B, such that AB:BC is 3:5?

List the roots of the parabola: y = x² - 6x + 10 In other words, list the solutions of the equation: 0= x² - 6x + 10 H= • Your answers must be in exact form, do not give their decimal values. • Separate multiple roots with a comma.

Two long distance runners began an 18 3/4-mile run. They ran uphill for 5 5/8 miles, downhill 7 1/3 miles, and the rest of the course was level. Find the distance of the level portion of the course.

Exercise #3: The graph of the function y=x²-4x+1 is shown below. (a) State this function's y-intercept. (b) Between what two consecutive integers does the larger x- intercept lie? (c) Draw the horizontal line y=-2 on this graph. (d) Using these two graphs, find all values of x that solve the equation below: x²-4x+1=-2

The Royal Fruit Company produces two types of fruit drinks. The first type is 70% pure fruit juice, and the second type is 95% pure fruit juice. The company is attempting to produce a fruit drink that contains 85% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 180 pints of a mixture that is 85% pure fruit juice?

Solve the following equation. y4 +12y² - 13 = 0

A ball is launched from a 1128.32-foot tall platform. The equation for the ball's height h at time t seconds after launch is h(t) = − 16t² + 6.4t + 1128.32 where h is in feet. When does the object strike the ground?

A box with an open top has a square base and four sides of equal height. The volume of the box is 144 ft³. If the surface area is 160 ft^2, find the dimensions of the box.

Please number your responses to the questions as they are shown (1 and 2). Tanya is given the graphs of the following functions. The functions f(x) and g(x) are linear, and the function s(x) is quadratic. f(x) = 3x - 8 g(x) = -2x + 5 s(x) = 4x² - 9x + 2 Tanya is then asked to find the graph of (f .g)(x) and the graph of (g.s)(x). For each combined function, she is given four options to choose from. 1. What clues will help Tanya identify the correct graph of (f. g)(x) 2. What clues will help Tanya identify the correct graph of (g.s)(x)

We are standing on the top of a 512 feet tall building and launch a small object upward. The object's vertical position, measured in feet, after t seconds is h(t) = -16t² +64t + 512. What is the highest point that the object reaches? feet

Determine if the following sets of quadratics are equivalent. Choose true or false. x-10x+14 = 0 and (2x-10)2 =156 (x-10)² = 68 and ² - 20x=-32 x² - 6x=247 and (x-3)² = 256 (x + 5)² = 65 and x² = 90 - 10x

Use the long division method to find the result when 3x³ + 5x² - 15x+7 is divided by x - 1.

Answer the following parts. (a) Solve x² - 7x + 10 = 0. (b) Solve (x-3)² - 7(x-3) + 10 = 0. Compare the solutions to part (a). (c) Solve (x + 2)² - 7(x + 2) + 10 = 0. Compare the solutions to part (a). (d) Solve (x-4)² - 7(x-4) + 10 = 0. Compare the solutions to part (a). (e) Write a generalization for the solution of (x-a)² - 7(x-a) + 10 = 0.

Consider the following expression: 5x2 +8 Step 1 of 2: The given expression is a polynomial. Determine if the polynomial is a monomial, binomial, or trinomial.

For the quadratic function f(x) = 2x² + 24x + 9, (a) Use completing the square to write the function in the form f(x)= a(x-h)²+k. (b) Use your answer to (a) to identify the vertex.

Where is the function f(x)=x² increasing? Where is it decreasing?

Solve the following equation using the quadratic formula. x² +9x+3=0 Using the standard form of a quadratic equation (ax² +bx+c= 0) so that a > 0, identify each of the following: a= (use a positive real number) b = C = Use the quadratic formula and simplify fully. The solution set is. (Simplify your answer, including any radicals and i as needed. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) The approximate solution set is {} (Separate values with a comma. Type each approximate value, rounded to 3 decimal places.)

Solve using elimination. x^2 + y2 = 41 x^2-y2= 9 x = 5, y = -4; x = 5, y = 4 or (5,-4), (5, 4) x = 5, y = 4; x = 4, y = 5; x = -5, y = -4; x = -4, y = -5 or (5, 4), (4, -5), (-5, -4), (-4, -5) x = 5, y = 4; x = -5, y = 4; x = 5, y = -4; x = -5, y = -4 or (5, 4), (-5, 4), (5,-4), (-5, -4) x = -5, y = -4; x = -4, y = -5 or (-5, -4), (-4,-5)

The equation y = (-16t-2)(t-1) represents the height in feet of a beach ball thrown by a child as a function of time, t, in seconds. 1. Find the zeros of the function. Explain or show your reasoning. 2. What do the zeros tell us in this situation? Are both zeros meaningful? 3. From what height is the beach ball thrown? Explain or show your reasoning.

Use the quadratic formula to solve for x. 3x²+6x = -1

Determine the type and number of solutions for the equation. x2 + 3x=8 Choose the type and number of solutions. A. Imaginary solutions, 2 B. Rational solutions, 2 C. Irrational conjugates, 2 D. Repeated solution, 1

Solve the equation x² + 9x - 30 using the Quadratic Formula. Give your answers as two separate numbers in exact form.