Quadratic equations Questions and Answers

Cosider the quadratic function y =x² - 4x - 3. The vertex is the point_____ The equation of the line of symmetry is_____ The vertical intercept is the point_____ The horizontal intercept(s) is/are the point(s)___

Which of the following statements is true for the quadratic equation x² - 16x+64 = 0? The equation has no solutions. The equation has two solutions. It's impossible to determine how many solutions the equation has. The equation has one solution.

Find allercepts and y-intercepts of the graph of the function. f(x)=3x² +17x+20 If there is more than one answer, separate them with commas. Click on "None" if applicable.

A frog with bionic legs leaps from a stump with an initial velocity of 64 ft/sec. It is determined that the height of the frog as a function of time can by modeled by h (t) = -16t² + 64r + 3. What is the maximum height? 131 ft 99 ft 67 ft 195 ft

Consider the Quadratic function f(x) = x² – 3x - 18. Its vertex is Its largest x-intercept is x = Its y-intercept is y =

The polynomial of degree 4, P(x) has leading coefficient 1, has a zero of multiplicity 2 at x = 4, a zero of multiplicity 1 at a x=0, and a zero of multiplicity 1 at x = - 4 Find a possible formula for P(x).

Caleb made a round-trip journey of 160 miles in each direction. Caleb's rate of travel to his destination was 15 mph slower than the rate of travel back home. His whole travel time was 10.4 hours. A) Set up the chart: (Use x as the going rate in the equation.) distance rate time going _______ x ________ returning ________ ________ ________ total ________ ________ _________ B) What is an equation that can be used to solve this problem? ____________ C) What was Caleb's rate of travel going to his destination? _________mph D) What was Caleb's rate of travel on his way home? ____________mph

Solve the equation 10z^2 + 11z – 6 = 0. Write your answers as a list of integers or reduced fractions, with your answers separated by (a) comma(s). For example, if you get 4 and -2/3 as your answers, then enter 4,-2/3 in the box.

Bob is thinking deeply about the following equation: y= ax^2 + c He comes to the conclusion that if 'a and 'c' have the same sign that there will be no x-intercepts. His is conclusion correct? If yes, justify his reasoning. If no, provide a counterexample.

Solve by completing the square. X^2 + 16x +41 = 0 Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.

Solve by completing the square. k^2 + 18k - 25 = 0 Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth,

Solve by completing the square. p^2 - 24p = -19 Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.

For the equation, (a) solve for x in terms of y, and (b) solve for y in terms of x. 6x² - 2xy + 3y² = 8 (a) Solve for x in terms of y. x = y+√(48 - 17y²)/6, y- √(48 - 17y²)/6 (Use a comma to separate answers as needed. Do not factor.) (b) Solve for y in terms of x. y= ▢ (Use a comma to separate answers as needed. Do not factor)

Chris operates a small sign-making business. He finds that if he charges x dollars for each sign, he sells 40 - x signs per week. What is the smallest number of signs that he can sell to have an income of $256 in one week?

Solve the equation by making an appropriate substitution. x4-40x² + 144= 0 Make an appropriate substitution and rewrite the equation in quadratic form. Let u = x², then the quadratic equation in u is u²-40u + 144 = 0 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is B. The solution set is 0.

Find the quadratic function y = ax²+bx+c whose graph passes through the given points. (2,-20), (-3,30), (1, -14) y=

Select the correct answer. Mr. Waller owns a company that manufactures decorative statues. The revenue earned, in thousands of dollars, by the company each year over an eight-year period is modeled by this quadratic function. r(t) = -3.22t² + 40.63t +11.17

Solve the equation using the quadratic formula. x²-2x+17=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 by completing the square. x² + 12x - 5 =0 x = 6-√41 or x = 6 + √41 x=-6-√41 or x = −6+ √41 x = -6√31 or x = −6+ √31 x= 6-√31 or x = 6 + √31

Solve 49x² - 36 = 0 x = 6 or x = -7 x=6/7 orx = -6/7 x= - 6/7 x = 6/7

Select the axis of symmetry and y-intercept of f (x) = -x² + 4x + 1 (0, -1) (0,-5) x=-2 x=-1 x=0 (0, 1) x=3 (0,8) (0, 12) x=2 x=4

Solve by factoring: 3x^2 + 7x + 2 = 0 x =1/3 orx = 2 x = -1/3 or x = 2 x=1/3 orx = -2 x= -1/3 or x = -2

What are the x-intercepts of the function f (x) = 2x² + 7x-4? x=-1/2₁x = 4 x = 1/2, x=-4 x=-8, x = 1 x=4,x=-7

Use factoring to solve: 7x² + 8x + 1 = 0 x = -7 or x = 1/7 x = 1 or x = 1/7 x = -1 or x = -1/7 x = -1 or x = 1/7

Find the missing value "c" to create a perfect square trinomial for x² + 16x + c 64 4 -4 08

Factor the perfect square trinomial: x² - 34x + 289 (x-17) (x + 17) (x-34)² (x-17)² (x + 17)²

Rewrite the equation y =-2x² + 20x + 31 in graphing form by completing the square. y=-2 (x - 5)² - 19 y=-2 (x - 5)² +81 y=2(x + 5)² – 19 y = -2(x + 5)² +56 None of the other answers

A certain electronics manufacturer found that the marginal cost C to produce x DVD/Blu-ray players can be found using the equation C = 0.03x² - 4x + 800. If the marginal cost were $1039, how many DVD/Blu-ray players were produced?

Find all the roots and check the answer. 7x² +78x+11=0

Which equation models the same quadratic relationship as function ? f(x) = 2x² - 12x + 11 A. y = 2(x + 6)² + 2 B. y = 2(x − 6)² + 5 C. y = 2(x - 3)² - 7 D. y = 2(x + 3)² - 7

Use the quadratic model d= -3p2 + 168p 315 to predict d if p equals 15. 1845 2160 2880 1530

The polynomial of degree 4, P(x) has a root of multiplicity 2 at x = 1 and roots of multiplicity 1 at x = 0 and x = - 4. It goes through the point (5, 72). Find a formula for P(x).

What substitution should be used to rewrite x8-3x4+2=0 as a quadratic equation? u = x² u=x4 u=x8 u = x16

One solution of the quadratic function f ls-5-7i. Which statement is true about this function? Another solution of function f is 5 + 7i. Another solution of function is 5 - 7i Function f has no other solutions. Another solution of function f is -5 + 7i.

Open the graphing tool from your tools and graph this system of equations. Then approximate the solutions to this system. y = 3x²+x-6 y = x - 4

Solve the equation x² - 4x+6=0 by completing the square.

For the following polynomial function, find (A) the degree of the polynomial, (B) all x-intercepts, and (C) the y-intercept. f(x) = (3x + 2)4(x − 5)5 (A) The degree of the polynomial is.

Consider the function f(x)=-3x² + 12x-9. a. Determine, without graphing, whether the function has a minimum value or a maximum value. b. Find the minimum or maximum value and determine where it occurs. c. Identify the function's domain and its range.

Use the Rational Zero Theorem to list all possible rational zeros for the given function. f(x) = 5x4 +4x³-12x² - 4x-10 Choose the answer below that lists all possible rational zeros.

A toy rocket is launched straight up from the top of a building. The function that models the height as a function of time is h (t) = -16t² + 200 + 50. At what height was the rocket launched? 16 ft 50 ft 200 ft 25 ft

Use the quadratic formula to solve the equation: 4x² - 26x - 42 = 0 Ox= 132-√337/4 or x = -13-2√//127/4 Ox= 13+√337/4 or x = -13+2√127/4 Ox= 13+2/127/4 or x = -13+2√/337/4 Ox= 13-2√//127/4 or x = -13-2√//127/4

A rock falls from a tower that is 102.9 m high. As it is falling, its height is given by the formula h = 102.9-4.91². How many seconds will it take for the rock to hit the ground? (h = 0) 2160.9 sec 4.6 sec 9.9 sec 10.1 sec

Find all the roots. 22x² - 15x=0 x = (Use a comma to separate answers. Type repeated roots only once.)

Which of the following sets contains all roots of the polynomial F(x) = 2x³ + x²-3x? A. (0,1,3/2) B. (-3/2,0.1) C. (-3/2,1) D. (-1.-3/2)

Which of the following is a root of the polynomial function below? F(x) = x² + 3x² -5x-4 A. 1/2 - √5/2 B. 4 C. 3 D. 1/3 + √5/3

The following is the student's incorrect work in solving a quadratic using the zero product property. Explain the student's mistake. Step 1: x²-3x - 4 = 8 Step 2: (x-4) (x + 1) = 8 Step 3: x 4 = 8 or x + 1 = 8 Step 4: x= 12 or x = 7 -

Which of the following polynomials is in standard form? A. F(x) = 5x+2x³ - x² - 3 B. F(x) = -3-x²+2x³ +5x C. F(x) = 2x³ -x +5x-3 D. F(x) = -3 +5x-x²+2x³

Find a polynomial f(x) of degree 4 with real coefficients and the following zeros. -1 (multiplicity 2), 3+2i

Which of the following shows the equation below rewritten in the form ax² +bx+c=0? (3x)² = 8(x-1) A. 3x²-8x+8 = 0 B. 9x² -8x+8=0 C. 9x² +8x-8=0 D. 3x² +8x-8=0

Which statement about k(x) = -x² - 2x + 15 is true? F The zeros are -3 and 5, because k(x) = -(x+3)(x - 5). G The zeros are -5 and 3, because k(x) = -(x + 5)(x-3). H The zeros are -5 and -3, because k(x) = -(x + 5)(x+3) J The zeros are 3 and 5, because k(x) = -(x-3)(x - 5).