Quadratic equations Questions and Answers

Consider the parabola given by the equation: Find the following for this parabola: y = x² + 6x - 8 A) The vertex = B) The y intercept is the point (0, C) Find the two values of that correspond to the x intercepts of the parabola and write them as a list, separated by commas: x = Round your answer(s) to two decimal places.

Consider the parabola given by the equation: f(x)=x²-12x + 13 Find the following for this parabola: A) The value of f(-5): B) The vertex = C) The y intercept is the point (0, D) Find the two values of a that make f(x) = 0. Round your answers to two decimal places. Write the values as a list, separated by commas:

Determine the number and type of solutions for the equation 2x2 + 5x + 5 = 0 Two different irrational-number solutions One repeated irrational-number solution One repeated rational-number solution Two different rational-number solutions Two imaginary-number solutions

Find all real solutions of the equation 3s² = 75. Write your answers as a list, using a comma to separate answers.

Find all real solutions of the equation 9t²-7=29. Write your answers as a list, using a comma to separate answers.

A parabola has a vertex at the point (-2, -3) and an x-intercept at (1, 0). Find the other x-intercept. You must justify your answer for credit.

Consider the quadratic function f(x)= -x2 - x +20 Determine the following: (enter all numerical answers as integers, fractions, or decimals): The smallest (leftmost) -intercept is = The largest (rightmost) a-intercept is= The y-intercept is y= The vertex is The line of symmetry has the equation

Solve using the quadratic formula. 0= 4x² + 11x + 4

Consider the quadratic function f(x) = x² + 2x − 3. Determine the following: (enter all numerical answers as integers, fractions, or decimals): The smallest (leftmost) z-intercept is a = The largest (rightmost) -intercept is a = The y-intercept is y = The vertex is The line of symmetry has the equation

A person standing close to the edge on top of a 108-foot building throws a ball vertically upward. The quadratic function h(t) = − 16t² + 132t + 108 models the ball's height about the ground, h(t), in feet, t seconds after it was thrown. a) What is the maximum height of the ball? b) How many seconds does it take until the ball hits the ground?

Find the critical numbers of the function f(x) = − 12x^5 + 75x^4 + 80x³ + 6 and classify them using a graph.

The drama club is selling tickets to their play to raise money for the show's expenses. Each student ticket sells for $7 and each adult ticket sells for $9.50. There was a total of $883.50 in revenue from all ticket sales and the drama club sold 27 more adult tickets than student tickets. Determine the number of student tickets sold and the number of adult tickets sold.

Skylar repairs washing machines. Her revenue, in dollars, can be modeled by the equationy = 80 +24x, where x is the number of hours spent repairing microwaves. Her overhead cost, in dollars, can be modeled by the equation y=x²-100, where x is the number of hours spent repairing washing machines. After how many hours does she break even?

Solve the equation x+1/x-1 = -2/x+3 + 8/x2+2x-3 List all valid solutions, separated by commas.

Solve the rational equation: x+56/x = 15

A model rocket is launched with an initial upward velocity of 70 m/s. The rocket's height h (in meters) after t seconds is given by the following. h=70t-5t² Find all values of t for which the rocket's height is 35 meters. Round your answer(s) to the nearest hundredth. (If there is more than one answer, use the "or" button.)

3) A movie theater charges $8.00 for adults and $5.00 for children. If there were 40 people altogether and the theater collected $272.00 at the end of the day, how many of them were adults? How many were children?

Analyze the polynomial function f(x) = x²(x + 4) using parts (a) through (e). (a) Determine the end behavior of the graph of the function. The graph of f behaves like y = x3 for large values of |x|. (b) Find the x- and y-intercepts of the graph of the function. The x-intercept(s) is/are 0,-4. (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 0. (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 0,-4. (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 of the function is of multiplicity, so the graph of f at x = the x-axis at x = The greater zero of the function is of multiplicity, so the graph of f the x-axis

The revenue achieved by selling x graphing calculators is figured to be x(45-0.2x) dollars. The cost of each calculator is $33. How many graphing calculators must be sold to make a profit (revenue - cost) of at least $160? A. Between 5 and 25 calculators B. Between 20 and 40 calculators C. Between 22 and 38 calculators D. Between 21 and 19 calculators

What is the vertex form of the equation? y=-x² + 12x-4

Select the value needed in the box in order for the expression to be a perfect square trinomial. x² +7x+ 3.5 7 12.25 14.5

Let f(x) = 9x^4 - 6x³ +23x + 25. Use Descartes' Rule of Signs to answer the following questions. (a) List the possible number of positive real zeros (counting multiplicities) of f(x): (b) List the possible number of negative real zeros (counting multiplicities) of f(x): (c) May anything definitive be said about the exact number of positive real zeros? Select an answer (d) May anything definitive be said about the exact number of negative real zeros? Select an answer There are no negative real zeros. There are exactly two real negative zeros. There is exactly one negative real zero. No conclusion may be made about the exact number of negative real zeros.

y=x² + 4x-5 Before we calculate important features of this quadratic function, identify a, b, &c. Remember, the standard form quadratic functions: y = ax^2 + bx + c. a = | b= C=

The owner of a video store has determined that the cost C, in dollars, of operating the store is approximately given by C(x)=2x² - 22x+780, where x is the number of videos rented daily. Find the lowest cost to the nearest dollar. A. $841 B. $659 C. $538 D. $720

Find all values of the variable x for which the rational expression is undefined. 3x + 5 / x² + 12x + 20 The expression is undefined when x = If there is more than one answer, write it as a list, using commas to separate your answers.

The function h(t) gives the height of a rock thrown off the Golden Gate Bridge in feet above the water at t seconds after it is thrown. h(t) = -16t² + 30t + 225 Question: How long after it's thrown will the rock hit the water?

The winner of a 10-mile bicycle race finishes 10 minutes ahead of a teammate and travels, on average, 10 miles per hour faster than the teammate. Find the average speed of each racer.

Solve the equation using the quadratic formula. x² +10x+21=0

Solve the equation using the quadratic formula. x² + 10x + 24 = 0 The solution set is (Simplify your answer. Type an exact answer, using radicals and i as needed. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)

Solve the equation by factoring. 9x² +21x-8=0 The solution set is (Use a comma to separate answers as needed. Type each solution only once.)

Solve the equation using the quadratic formula. 5x^2 = 2x+4

A community theater uses the function p (d)=-4d^2 + 200d - 100 to model the profit (in dollars) expected in a weekend when the tickets to a comedy show are priced at d dollars each. Write and solve an equation to find out the prices at which the theater would earn $1,500 in profit from the comedy show each weekend.

Select the best choice for the definition for vertex. A. The graph of a quadratic function that is a U-shaped curve. B. Is defined by an ordered pair and is considered the minimum point or the maximum point. C. A vertical line that passes through the vertex of the graph of a quadratic function. D. A term that describes the x-intercept(s) of the graph of a quadratic function.

Use the ALEKS graphing calculator to solve the system of equations. x² + y² = 22 y=9/7 x+ 5/7 Round to the nearest hundredth. If there is more than one solution, use the "or" button. If applicable, click on "No solution". (x,y)= No solution

Which equation represents a quadratic function with a leading coefficient of 2 and a constant term of -3?

Select the best choice for the definition of roots, zeroes or solutions for the graph of a quadratic function. * A. A vertical line that passes through the vertex of the graph of a quadratic function. B. A term that describes the x-intercept(s) of the graph of a quadratic function. C. The graph of a quadratic function that is a U-shaped curve. D. Is defined by an ordered pair and is considered the minimum point or the maximum point.

Which of the following shows that polynomials are closed under addition when two polynomials 4x + 6 and 2x²-8x-4 are added? (1 point) a. 2x²-4x+2 will be a polynomial b. 2x²-4x+2 may or may not be a polynomial c. 2x²-12x-10 will be a polynomial d. 2x²-12x-10 may or may not be a polynomial

Solve the equation using the quadratic equation. x² = 2-6x

Find all solutions by factoring. 3w² - 13w=10

Solve for x. (x + 1)² = 2 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. x= (Simplify your answer. Type an exact answer, using radicals as needed. Use a comma to separate answers as needed.) B. The equation has no real solutions.

A rocket is fired upward with an initial velocity v of 70 meters per second. The quadratic function h(t) = -5t² + 70t can be used to find the height h(t) of the rocket, in meters, at any time t in seconds. Find the time it takes for the rocket to reach its maximum height. What is the maximum height reached by the rocket? The rocket reaches the maximum height at The maximum height that the rocket will reach is meters.

A quadratic function f is given. f(x) = -x² + 12x (a) Express f in transformation form. f(x) = (b) Find the vertex and x- and y-intercepts of f. (If an answer does not exist (x, y) = vertex x-intercepts y-intercept (x, y) = (x, y) = (x, y) = ( (smaller x-value) (larger x-value)

Solve by comparing the square : x2 + 8z - 2 = 0 f(x) = 5x2 - 1 Is it odd, even or neither A ball is thrown straight up, from 3 m above the ground, with a velocity of 14m/s. When does it reach it's maximun height? H (t) = 3 +14t-5t2

Compute the discriminant of 8x² = -7-x. The discriminant is: How many real solutions does the equation, 8x² = -7-x, have? 2 non-real solution One real solution Two real solutions None of the above

Solve the quadratic equation by completing the square: t² + 8t - 27 = 41 Give the equation after completing the square, but before taking the square root. Your answer should look like: (t - a)² = b The equation is: List all solutions to the equation in simplest radical form, separated by commas. The solutions are: t =

Follow the method in Step 1 to determine if the fourth expression is a perfect square trinomial. The first term and the third term of the fourth trinomial, 4x^2 + 12x + 9, are perfect squares. 4x² = (2x)² 9 = (3)² Because the x-term is positive, if the trinomial is a perfect square, then it is the square of a binomial sum. Find the square of the binomial formed by the sum of the square roots of the perfect squares, (2x + 3)². You can use the distributive property to square the binomial. Or you can use the rule for squaring a binomial sum, (a + b)² = a² + 2ab + b², with a = 2x and b = 3. Compare the original trinomial to the square of the binomial.

Two pipes can fill a tank in 64 minutes if both are turned on. If only one is used, it would take 54 minutes longer for the smaller pipe to fill the tank than the larger pipe. How long will it take for the smaller pipe to fill the tank? (Round your answer to the nearest tenth.)

Given that point (a,b) is a solution to an equation, which of the following statements must always be true? A. The point (a,b) lies on the graph of the equation. B. The point (a,b) lies on the graph of the equation where it crosses the y-axis. C. The point (a,b) lies on the graph of the equation where it crosses the x-axis. D. The position of the point (a,b) with respect to the graph of the equation cannot be determined.

Given that 2 - 2i is a zero, factor the following polynomial function completely. Use the Conjugate Roots Theorem, if applicable. f(x) = x4 - 10x³ + 25x² - 20x - 56

A jewelry store sells 168 diamond bracelets per month at $1100 each. The owners estimate that for each $55 increase in price, they will sell 6 fewer diamond bracelets per month. Find the price per diamond bracelet that will maximize revenue.