Quadratic equations Questions and Answers

A ball is thrown upward from the top of a 48-foot-high building. The ball is 64 feet above ground level after 1 second, and it reaches ground level in 3 seconds. The height above ground is a quadratic function of the time after the ball is thrown. Write the equation of this function.

Which shows the equation below written in the form ax2+bx+c=0? x² +7x+9=3 A. x²+4x+6=0 B. x² +7x+6=0 C. x² + 4x+12=0 D. x² +7x+12=0

Solve the quadratic equation by completing the square. x²+8x = -7 To complete the square, what number should be added to both sides of the equation? Type an integer or a simplified fraction.)

ok so for this problem we need to write the answer in interval notation, and in the answer key its [-5/3,2] and i understand where the points came from and why its using brackets but why doesn't it use union? like (-infini, -5/3]U[2, infini) (edited) 4. 3x²-x-10 ≤0

Use your graphing calculator to solve the equation graphically for all real solutions. x³4x²-3x + 14 = 0 Solutions: = Make sure your answers are accurate to at least two decimals.

Solve the equation. 3x+6/3 - 4x / X-2 =X Select the correct choice below and, if necessary, fill in the answer box to complete your A. The solution set is (Simplify your answer. Use a comma to separate answers as needed.) B. The solution is the empty set.

A cartographer used a scale of 1 inch:300 meters for the heights of different mountains. If the actual height of one of those mountains is 3,600 meters, what is its height on the map? 100 inches 1,080 inches 12 inches 108 inches

Solve equation by the quadratic formula. List the solutions, separated by commas. 2r² - 3r+13= 8

Consider the function y = 4x² + 8x-26. (a) Give the coordinates of the vertex of the graph of the function. (b) Graph the function on a window that includes the vertex.

A parabola that passes through the point (2, -37) has vertex (-8, 13). Its line of symmetry is parallel to the y-axis. Find equation of the parabola: y = When x = 12, what is the value of y: What is the average rate of change between x = -8 and x = 12:

Factor the polynomial f(x) = 2x³-5x² - 14x+8 given that x=4 is a zero of f(x). f(x) = (x-4) (2x + 1)(x - 2) f(x) = (x-4) (2x − 1)(x + 2) f(x) = (2x - 1)(x+2) f(x) = (x + 4) (2x + 1)(x − 2)

Use the quadratic formula to solve the equation 16x² + 32x + 25 = 0. Enter multiple answers as a list separated by commas. Example: 2 + 2i, 2 - 2i

What is the range of the polynomial function f(x) = -x4-2x³ + x +1?

Use the quadratic formula to solve the equation x² + 10x + 29 = 0. Enter multiple answers as a list separated by commas. Example: 2 + 2i, 2 - 2i

Use a graphing utility to find or approximate solution(s) of the given equation. 20x+5=24x² + 6x Select the correct choice below and, if necessary, fill in the answer box to complete your answer. A. The solution (s) is/are x = (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. The equation has no solution.

Consider the function y = 30x - 3x² (a) Give the coordinates of the vertex of the graph of the function. (b) Graph the function on a window that includes the vertex. (a) The vertex of the function is . (Type an ordered pair.)

Give the coordinates of the vertex of the graph of the function. Graph the function on a window that includes the vertex. y = (x + 2)² +1 The vertex is (Simplify your answer. Type an ordered pair.)

Use a graphing utility to find or to approximate the x-intercepts of the graph of the function. y = 3x² - 14x+8 Select the correct choice below and, if necessary, fill in the answer box to complete your answer A. The x-intercept(s) is/are x = (Simplify your answer. Use a comma to separate answers as needed. Type an integer or decimal rounded to four decimal places as needed.) B. There is no x-intercept.

Suppose that the functions q and r are defined as follows. q(x)=-2x+2 r(x)=x² +1 Find the following. (qor) (2) = (roq)(2) =

For the following function, f(x)=x²-3x-10 : (a) Find the values of x for which f(x) = 0. (b) Find f(0).

Analyze the polynomial function f(x) = -3(x+2)(x-4)³ using parts (a) through (e). (a) Determine the end behavior of the graph of the function. The graph of f behaves like y= for large values of |x| (b) Find the x- and y-intercepts of the graph of the function. The x-intercept(s) is/are (Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed. Type each answer only once.) The y-intercept is (Simplify your answer. Type an integer or a fraction.) (c) Determine the zeros of the function and their multiplicity. Use this information to determine whether the graph crosses or touches the x-axis at each x-intercept. The zero(s) of f is/are (Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed. Type each answer only once.) The lesser zero is a zero of multiplicity, so the graph of f the x-axis at x = The greater zero is a zero of multiplicity, so the graph of f the x-axis at x =

E Homework: Homewor Answer the questions about the following function. f(x)=3x²-x-2 (a) Is the point (-1,2) on the graph of f? (b) If x= 2, what is f(x)? What point is on the graph of f? (c) If f(x) = -2, what is x? What point(s) are on the graph of f? (d) What is the domain of f? (e) List the x-intercept(s), if any, of the graph of f. (1) List the y-intercept, if there is one, of the graph of (a) Choose the correct answer below. A. Yes, because substituting x = 2 into the given equation results in -1. B. No, because substituting x=2 into the given equation does not result in -1 C. No, because substituting x = -1 into the given equation does not result in 2. D. Yes, because substituting x = -1 into the given equation results in 2. (b) If x=2, f(x) =

Solve the following quadratic equations when the "b" term is missing.

A backyard pool has a concrete walkway around it that is 4 feet wide on all sides. The total area of the pool and the walkway is 950 ft. If the length of the pool is 6 feet longer than the width, find the dimensions of the pool. The length of the pool is feet and the width is feet.

olve the equation by making an appropriate substitution. 36x=85x²-49

Given the polynomial f(x) = -2x³-7x² + kx + 4, find the value of k given that x=1 is a zero of the polynomial. 0 -9 10 5

Solve the following equation by making an appropriate substitution. (x + 5)² +9(x+5) +18=0 Make an appropriate substitution and rewrite the equation in quadratic form. Let u= x +5, then the quadratic equation in u is u² +9u+18=0. Solve the equation. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is (Simplify your answer. Use a comma to separate answers as needed.) B. The solution set is the empty set.

Factor. 20a²-11a-3 Select the correct choice below and, if necessary, fill in the answer box within your choice. A. 20a²-11a - 3 = B. The polynomial is prime.

Factor. 25q²-40qd+ 16d² Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. 25q²-40qd +16d² = (Factor completely.) B. The polynomial is prime.

Find the x-coordinate of the vertex, y-coordinate of the vertex, and the z-intercepts. x-coordinate of the vertex - x =-b/2a

Find all values of x such that y=0. y = [x+4 / (7x-28)] -[4 / (x+4)] -2/7 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The value(s) of x for which y=0 is/are. (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. y=0 for all values of x. C. There are no values of x for which y = 0.

The quadratic expression (x - 1)^2 - 25 is written in vertex form. a. Write the expression in standard form. b. Write the expression in factored form.

When the sum of 3 and twice a positive number is subtracted from the square of the number, 0 results. Find the number.

When the sum of 4 and twice a positive number is subtracted from the square of the number, results. Find the number. The number is (Simplify your answer. Type an exact answer, using radicals as needed.)

Solve the following equation, upload a picture of your solution showing the method you chose to solve the quadratic. Make sure your work is neat and organized. 3x²-5x-7=0

A rocket is fired upward with a velocity (v) of 96 feet per second. Find how many seconds it takes for the rocket to reach a height of 128 feet. Use the quadratic equation S = - 16t² +96t.

What is (are) the x-value(s) that solve the system of equations y = x² and y = 2x - 1? x = 1 x=-2 x= -1, -2 x = 1, 2 No solution.

Sketch the graph of the quadratic function. f(x) = 3x² + 2 Indicate the coordinates of the vertex, the y-intercept and \ the x-intercepts (if any). (If an answer does not exist, enter DNE. If there are multiple x-intercepts, enter your answers as a comma-separated list.) (x, y) = Graph Layers After you add an object to the graph you can use Graph Layers to view and edit its properties.

x² + Bx +49 Find the value of "B" that will make the expression a perfect square trinomial Write the trinomial as a product of two factors

Given the polynomial functions j(x) and k(x), find k(x) - j(x). j(x) = x² - x k(x) = 2x³ + x² – 1 -2x³x - 1 x³ + x 1 2x³ + x-1 2x³ + 2x² + x −1

Write the quadratic equation in all 3 forms given the relevant data: Given a = 2, b = -4, c = -16, Vertex: (1,-18), x-intercepts: (4,0) and (-2,0)

Write the quadratic equation in standard form. 22=11x-4x² The quadratic equation in standard form is

Use the remainder theorem to find P(-1) for P(x)=2x³+4x² +9. Specifically, give the quotient and the remainder for the associated division and the

Factor the polynomial f(x) = x³ - 2x² - 9x + 18 given that x=2 is a zero of f(x). f(x) = (x-2)(x - 3)(x+3) f(x) = (x − 3)(x + 3) f(x) = (x-2)(x - 3)² f(x) = (x + 2)(x − 3)(x+3)

Use Descartes Rule of Signs to determine all possible combinations of real and imaginary zeros for the polynomial f(x) = x¹ x³ + 8x - 8. Then find all the real and imaginary zeros of the polynomial given that (x-1) is a factor of the polynomial. All work must be shown for credit.

Use the AC Method to factor x² + 14x + 48 Split the linear term, writing x2 + 14x +48 as the sum of two binomials: (be careful about how you choose to split 14x, or the AC method won't work!) Factor out the GCF of each binomial: Complete the process of factoring by grouping:

In this problem we will give a graph sketch of f(x) = x4 - 4x². (a) Factor f(x), find the roots. (b) For each root from part (a), give the degree. (c) Determine the sign decomposition for f(x) (aka where f(x) is positive and negative). (d) Graph f(x):

Solve the following equation by factoring. x²-81=0 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is B. There is no solution.

An epidemiological study of the spread of a certain influenza strain that his a small school population found that the total number of students, P, who contracted the flut days after it broke out is given by the model P = -t2 + 13t+130, where 1 < t < 6. Find the day that 160 students had the flu. Recall that the restriction on t is at most 6.

Use Descartes Rule of Signs to determine the possible combinations of real and imaginary zeros of each polynomial. Then, identify all the zeros of each polynomial. Please show all work for full credit. 1. f(x) = x³ + 2x² - 16x - 32 2. f(x)= x³ + x² + 16x + 16