Quadratic equations Questions and Answers

A smart-phone is thrown upwards from the top of a 240-foot building with an initial velocity of 32 feet per second. The height h of the smart-phone after t seconds is given by the quadratic equation h=16t² + 32t + 240. When will the smart-phone hit the ground?

1) Determine the equation of a quadratic function in standard form given zeros x = 5, x = -12 and point (0, -60). 2) Determine the equation of a quadratic function in standard form given zeros x = -4, x = -2 and point (-3,-1).

Find the zeros of the function f(x) = x² -11.2x+28.9. Round values to the nearest hundredth (if necessary).

Find the zeros of the function f(x) = x² + 7.4x + 7. Round values to the nearest hundredth (if necessary).

Using the equation editor or uploading a picture: Solve by using the complete the square method: 9x² - 28x-54= -10x Make sure to show all the steps for solving this problem.

Write the quadratic equation whose roots are -6 and -1, and whose leading coefficient is 2. (Use the letter x to represent the variable.)

A company has determined that when x hundred dulcimers are built, the average cost per dulcimer can be estimated by C(x) = 0.1x2 -0.3x + 1.525, where C(x) is in hundreds of dollars. What is the minimum average cost per dulcimer and how many dulcimers should be built to achieve that minimum? The minimum average cost per dulcimer is

Solve 4z²-1z - 10 = 0. Round each answer to two decimal places. Enter your answers as a list of numbers, separated with commas. Example: 3.25,4.16

(5 points) Suppose f(x) = -x² + 10x - 16. (a) For which values of x is the function f(x) positive? Enter your answer using inequalities. help (inequalities) (a) For which values of x is the function f(x) negative? Enter your answer using inequalities. help (inequalities)

(7 points) You are given a scenario which can be modeled by a quadratic function. Each part of the scenario corresponds to a different part of the graph of the quadratic function. Choose the part of the graph that gives information about the specified part of the scenario. SCENARIO: The height of a baseball t seconds after being hit is modeled by: h(t)=-16t² + 75t +3.5 Parts of the scenario: A) The height of the ball when it is hit. B) The time when the ball hits the ground. C) A part of the graph unrelated to the scenario. D) The maximum height of the ball. E) The time when the ball is at its highest.

Ariana is a songwriter who collects royalties on her songs whenever they are played in a commercial or a movie. Ariana will earn $40 every time one of her songs is played in a commercial and she will earn $110 every time one of her songs is played in a movie. Ariana earned a total of $500 in royalties on 9 commercials and movies. Write a system of equations that could be used to determine the number of commercials and the number of movies on which Ariana's songs were played. Define the variables that you use to write the system.

Solve the quadratic equation by completing the square. x²-18x+74=0 First, choose the appropriate form and fill in the blanks with the correct numbers. Then, solve the equation. Round your answer to the nearest hundredth. If there is more than one solution, separate them with commas.

Consider the equation below. x3 - 3x² − 4 = 1/r-1 + 5 The solutions to the equation are approximately x =0.91 and x = 5.37 3.36 3.69 xt

A ball is thrown from an initial height of 5 feet with an initial upward velocity of 35 ft/s. The ball's height h (in feet) after t seconds is given by the following. h=5+35t-167 Find all values of t for which the ball's height is 23 feet. Round your answer(s) to the nearest hundredth. (If there is more than one answer, use the "or" button.)

What is the lower bound of the polynomial function? ƒ (x) = x² 4x³ + 9x² - x - 14

Divide using synthetic division. (7x²+x-8)+(x-1) (7x²+x-8) + (x-1)=0 (Simplify your answer. Use integers or fractions for any numbers in the expression. Do not factor.)

If a quadratic equation has roots X = 7 and x = -3, which of the following could represent the actual quadratic equation? y = (x + 7)(x + 3) y=(x-7)(x − 3) y = (x + 7)(x − 3) y = (x-7)(x + 3)

Every quadratic will have a vertex. True False