Quadratic equations Questions and Answers

Find the formula, in standard form y = ax² + bx+c, for a quadratic that has roots at x = -9 and x = 5, and has leading coefficient of 1. y=

A patient has an illness that typically lasts about 24 hours. The temperature, T, in degrees Fahrenheit, of the patient t hours after the illness begins is given by: T(t) = -0.01t² +0.248t +97.2. Use your calculator to graph the function and answer the following questions. Round all answers to 1 decimal place. When does the patient's temperature reach it maximum value? What is the patient's maximum temperature during the illness?

Which expression is the same as x-12+3x² 3x² + x + 12 3x² + x - 12 -3x² + x + 12 3x² - x + 12

Suppose the average number of vehicles arriving at the main gate of an amusement park is equal to 10 per minute, while the average number of average waiting time in minutes for each vehicle at the gate is given by f(x) =x-5/x²-10x, where x> 10. (a) Estimate the admittance rate x that results in an average wait of 30 seconds. (b) If one attendant can serve 4 vehicles per minute, how many attendants are needed to keep the average wait time 30 seconds or less? (a) Estimate the admittance rate x that results in an average wait of 30 seconds. The admittance is about vehicles per minute. (Round to the nearest tenth as needed.)

After using the discriminant on a quadratic, a student got a positive number. What can the student determine from this info A The quadratic has one x- intercept. B The quadratic has two - intercepts. C The quadratic has no x-intercepts. D Nothing can be determined with this information.

Solve the following rational inequality x-6/x^2-64< 0. State your answer using interval notation. Use U for union and oo for ∞.

The vertex form of the quadratic function f(x) = -7x² +28x - 23 is ƒ (x) = a(x − h)² + k. - What is the value of a? What is the value of h? What is the value of k?

Graph the equation y = -x² - 10x - 24 on the accompanying set of axes. You must plot 5 points including the roots and the vertex.

Given the function f(x) = 3x² - 3x + 8. Calculate the following values: f(− 2) = f(− 1) = f(0) = f(1) = f(2)=

Solve the following equation using the quadratic formula. 2 4x = 2x + 3 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 following equation has two real solutions, one of which is zero. 9x² - 288x^3/4= 0 Find the other (non-zero) solution. Give your answer as a simplified integer or improper fraction, if necessary. Do not type 'x= ' in your answer.

Divide using the quotient rule. 42x²y/7xy²

A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find the time that the rocket will hit the ground, to the nearest 100th of second. y=16x² +124x + 127

Solve the following equation using the quadratic formula. 5x − 8x=4 ***** Points: 0 of 1 Next question 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.)

Add. For answer, simplify numerator, but write denominator in factored form. 6T 5 8z+16 4

Solve the equation for all values of x by completing the square. x² - 16 = -6x

Solve the equation using any method. Show your thinking. (2 poir Explain why you chose that method using academic vocabulary. ( x² 22x + 121 = 16 02 -

A population has a normal distribution. A sample of size n is selected from this population. Describe the shape of the sampling distribution of the sample mean for the following case. O The shape is skewed to the left. O The shape is skewed to the right. O The shape is normal. n = 21

Solve: 5/x² - 7x + 12=2/(x-3)+5/(x-4) No solution x=4 x=3 x -4

The height, in feet, of an object t seconds after being launched is given by the equation h = - 16t²+64t. How long does it take for the object to return to the ground? a. 1 second b. 2 seconds c. 3 seconds d. 4 seconds e. 5 seconds

Identify the axis of symmetry, min/max value, and y-intercept. y = x² +6x+16 Axis of Symmetry: x = - 3 Min Value = 7 y-intercept: 16 Axis of Symmetry: x = -7 Min Value =3 y-intercept: - 46 Axis of Symmetry: x = - 3 Min Value =7 y-intercept: -2 Axis of Symmetry: x = 4 Min Value =-6 y-intercept: - 22 There is no correct answer given.

Earl's bike shop makes and sells bikes and has a profit function of P(x) = -2x² +260x-5000, where P(x) is the profit in dollars from selling x bikes a) For this function P(30)= 1000. Explain what that means in the context of the situation. (4 pts) b) According to this model, can the shop earn $5,000 in profit? Justify your answer. (4 pts) c) How many bikes would the shop need to sell to break even? Round to the nearest whole number.(6pts)

The total fresh vegetables consumed per person per year can be modeled by V(t) = 0.2(t- 3)2 + 64.8 where V(t) is the total fresh vegetables consumed per person in pounds per year t years since 2010. Find when the minimum intake of fresh vegetables per person occurred? {final answer will be number only}

A golf pro practices his swing by driving golf balls off the edge of a cliff into a lake. The height of the ball above the lake (measured in meters) as a function of time (measured in seconds and represented by the variable t) from the instant of impact with the golf club is the following: h(t) = 58.8 + 19.6t - 4.9t² The expressions shown are equivalent: -4.9t² + 19.6t + 58.8 standard form -4.9(t-6) (t + 2) factored form -4.9(t - 2)² + 78.4 vertex form 1. Which expression is the most useful for finding how many seconds it takes for the ball to hit the water? Why? 2. Which expression is the most useful for finding how many seconds it takes for the ball to reach its maximum height? Why? 3. Which expression is the most useful for finding the maximum height of the ball? Justify your answer.

For the quadratic y = −3(x - 1)² + 2, the 2nd differences would be -6 cannot be determined 2 -3

In an archer shoos an arrow straight upward with initial velocity of 80 ft/sec from a height of 4 feet then it's height above the ground in feet at time t in seconds is given the function: h(t) = -8t² + 80t + 4 a. What is the maximum height reached by the arrow? b. How long does it take for the arrow to reach the ground?

Find the zeros of the function f(x) = -1.6x² + 19x - 53.1. Round values to the nearest hundredth (if necessary).

Supposed Aven drops a ball off the top of a 10 foot pool slide, and the ball follows the projectile h(t) = -16t² + 6, where t is the time in seconds, and h is the height of the ball. Her friend Riley needs to catch the ball between 2 feet and 5 feet off the top of the water. Between what two times should Riley try to catch the ball? * 2 sec and 5 seconds 0.25 sec and 0.5 sec 0.83 sec and 0.94 sec 1.4 sec and 3.2 sec

(2 points each) Guadalupe stands on a platform and tosses a penny in the air. Its height in feet off the ground is h. Its time in seconds in the air is t. The equation is h = -16t² + 112t + 128. a) How high is the penny after 2 seconds? b) How long will it take for the penny to hit the ground?

A diver jumps upward from the diving board and performs a double twist before entering the water. The function shown describes her height h(t) in feet above the water, t seconds after she jumps. h(t) = 10 + 40t - 16t² Question: When will she be 26 feet above the water?

A company sells widgets. The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the given equation. Using this equation, find out what price the widgets should be sold for, to the nearest cent, for the company to make the maximum profit. y = -34x² + 1542x - 10037

A company sells widgets. The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the given equation. Using this equation, find out the maximum amount of profit the company can make, to the nearest dollar. y=-6x²+600-5726

Suppose that a ball is thrown from the top of a 104-foot building. The function h(t) = - 16t2 +88t + 104 models the height in feet, h, of the ball t seconds after it is thrown. a) When does the ball hit the ground? The ball hits the ground after Select an answer ✓ b) Find the time(s) the ball will be 200 feet above ground. (You may use fractions or decimals. Use a comma to separate values, if necessary} The ball is 200 feet above ground after Select an answer ✓ c) The ball will be at its highest point after t = 2.75 seconds. Find the height of the ball at that time. The height of the ball after 2.75 seconds is Select an answer ✓

Suppose that a roll of toilet paper is thrown upward from the top of a 52-foot building with initial velocity of 96 feet per second. The function h(t) 16t2 +96t+52 models the height in feet, h, of the toilet paper roll t seconds after it is thrown. a) Determine the height of the toilet paper roll after 3 seconds. After 3 seconds, the toilet paper roll is Select an answer above the ground. b) When does the toilet paper roll hit the ground? The toilet paper roll hits the ground after Select an answer c) Determine when the toilet paper roll reaches 52 feet above the ground. The toilet paper roll will reach 52 feet at Select an answer

A toy rocket launch can be represented by a parabolic function. Your most recent launch for the science fair can be modeled by the function y = -4(x - 5)² + 125 where y is the height of the rocket and is the number of seconds since launch. Graph this function and include all of the points listed above, then discuss in context what the vertex and x-intercepts mean in context.

Find the discriminant of each quadratic equation then state the number and type of solutions. -m² + 6m - 19 = -10 O 72; one real solution O 0; two imaginary solutions 72; two real solutions O 0; one real solution O 0; two real solutions

A ball is thrown into the air with an upward velocity of 48 ft/s. Its height h in feet after t seconds is given by the function h = -16t² + 48t + 8. In how many seconds does the ball reach its maximum height? Round to the nearest hundredth if necessary. What is the ball's maximum height?

Determine if the function is quadratic. If it is, determine if the graph is concave up or concave down. Determine if the vertex of the graph is a maximum point or a minimum point. y = 3x² + 2x+5 Is the function quadratic? No Yes Is the graph concave up or concave down? Concave up Concave down Is the vertex of the graph a maximum point or a minimum point? Maximum point Minimum point

Factor the four-term polynomial by grouping. 4x²-8xy-3x+6y Select the correct choice below and, if necessary, fill in the answer box within your choice. A.4x²-8xy-3x+6y= B. The polynomial is not factorable by grouping.

Factor the trinomial completely. 2x² +12x+10 Select the correct choice below and fill in any answer boxes within your choice. O A. 2x² + 12x+10=(3) (Factor completely) O B. The polynomial is prime.

Factor the following trinomial: x² - 15x + 54.

Which expression(s) is/are a quartic function? SELECT ALL THE APPLY. ƒ(x) =−x (x + 1) (x − 5) (x+3) f(x) =- (x + 9) (x + 1) (x − 5) (x+3) f(x) = x³ - 0.15x+1 f(x) = x³ f(x)=x4-x²+2x–9 f(x) = 3x³ (x+2) f(x) = 4x² + x +56 f (x) = -10x4

Find the value of c that makes the expression a perfect square trinomial. x² + 24x + c a 144 b 12 c 36 d 576

The route that a trolley takes around a city can be represented by the functions x2 + y2 = 5. A train track's path can be described by the function 3x + y = 5. At which location(s) will the trolley and train meet? O(1, 2) and (2, -1) O(-1, 2) and (-2,-1) O(2, -1) and (-2,-1) O(-2, 1) and (-1,2)

A rectangle has an area of 384 square meters. Its width is eight meters less than twice the length. Let A be the area of the rectangle, L be the length and W be the width of the rectangle. (A) Express the area A of the garden as a function of one of its dimensions. You may use either the variable L or the variable W in your function, but you may not use both variables in the function. (For example: A = L2-5L or A = W² + 5W are acceptable but not A = L* W)

Consider the daily profit from the production and sale of x units of a product, given by P(x) = -3600+400x - 4x² dollars. a) Find the levels of production and sales that give a daily profit of $6000. b) How many units need to be produced to maximize the profit?

Solve the equation analytically for all complex solutions, giving exact forms in your solution set. Then, graph the left side of the equation as y, in the suggested viewing window and, using the capabilities of your calculator, support the real solutions. x4-37x² +36=0: [-10,10] by [-100,100] How many zeros are there? The zeros are x= (Use a comma to separate answers as needed.)

Given the quadratic equation -3v² + 10 = -2v Which of the following shows the equation in standard form, the value of the discriminant, and the correct number and type of roots? Standard Form: 3v²-2v-10-0 Discriminant: -84 2 Rational Roots Standard Form: 3v² - 2v10 = 0 Discriminant: 124 2 Irrational Roots Standard Form: 3v² - 2v 10 = 0 Discriminant: -84 2 Irrational Roots Standard Form: 3v²-2v-10-0 Discriminant: -124 2 Complex Roots

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).