For the quadratic function f(x)=x²+4x-12. answer parts (a) through (c). O down O up What are the coordinates of the vertex? The vertex of the parabola is (Type an ordered pair. Use integers or fractions for any numbers in the expression.) What is the equation of the axis of symmetry? The axis of symmetry is (Type an equation.) What is/are the x-intercept(s)? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA The x-intercept(s) is/are (Type an integer or a decimal. Use a comma to separate answers as needed.) OB. There are no x-intercepts. What is the y-intercept? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The y-intercept is. (Type an integer or a decimal.) OB. There is no y-intercept Use the graphing tool to graph the function. Click to enlarge graph (b) Determine the domain and the range of the function. The domain offis (Type your answer in interval notation.) The range of fis (Type your answer in interval notation.) (c) Determine where the function is increasing and where it is decreasing The function is increasing on the interval (Type your answer in interval notation.) The function is decreasing on the interval in intens (Type your answer in interval notation.) # AY C

Q: How many people are needed to guarantee that at least 4 people have a birthday in the same month?

A: This is an application of pigeon hole principle. According to pigeon hole principle, if there are n…

Q: A mass weighing 16 lb stretches a spring 3 in. The mass is attached to a viscous damper with a…

A: We have to find the position of the mass at any time t. We have to Determine the quasi-frequency and…

Q: F(x) = x²=2 Approximate this fun Xo=0, X₁=1 are initial values do this Up to 3- iteration? Using…

A:

Q: find the monthly mortgage loan payment for a $187,000 loan at 4.0% for 20 years.

A: The objective of this question is to calculate the monthly mortgage payment for a loan of $187,000…

Q: Prove by induction that Vn € {0, 1, 2, ...} and for any a + 1, =(n + 1)an + nan+1 (1-a)² 72 Σκακ k=1…

A: "Since you have posted multiple questions, we will provide the solution only to the first question…

Q: Hello, hoe about #2

A: The given function is in branch We can find Laplace transform by defination .

Q: c) d² y dt² +2+y=4t, y(0) = 0, y'(0)=5 dt

A: We have to find the solution of the differential equation.

Q: Prove by induction that Vk € N, S. 2k-¹e2dr = (k-1)!.

A:

Q: Solve the following system of equations for x, y, z using any of the methods that we have covered in…

A:

Q: Particular values for the function f(x) are given in the table below. X f(x) 9 18 Use the table to…

A: 918273645-9-15-20-19-6We hae to find:(a) a right-hand Riemann sum(b) a lift-hand Riemann sum

Q: Consider two circles in a plane. The first circle, C₁, has a radius of r₁ and is centered at point…

A: For the centers of the two circles C1 and C2 to coincide, the coordinates of their centers must be…

Q: Suppose a system of constant coefficient differential equations - Az has a 2 x 2 matrix A with Find…

A:

Q: Letf, g be continuous from R to R, and suppose that f(r) = g(r) for all rational numbers r. Is it…

A:

Q: Find the change of basis matrix [B]• B -{[B][] }; C {[³][7]} =

A:

Q: Use Green's Theorem to evaluate the following integral Let² dx + (5x + 9) dy Where C is the triangle…

A:

Q: 2.2. Show that this algorithm has an approximation ratio √2. More specifi- cally: The point found by…

A: In this problem, we are dealing with a set of points (xi,yi) for i=1,2,....,n in a 2D plane, each…

Q: Compute u • u, vou, and u u using the vectors u = 3 and v= 7

A:

Q: Use the Laplace transform to solve the given initial-value problem. [t, 0≤t<1 t≥ 1 y' + 6y = f(t),…

A: We have to Use the Laplace transform to solve the given initial-value problem.We use

Q: 10_M6A1. Show your steps and process for computational questions. For proofs, be sure to write in…

A: The objective of this question is to prove that the function q is a homomorphism, find the kernel of…

Q: 2. Assume that Σak <∞, prove that are converges uniformly on [-1,1].

A: We are given that ∑|ak|&lt;∞ , which means the series of absolute values of the coefficients…

Q: Using the method you described, what are the equilibrium points when m=85 and g=9.8? Please show…

A:

Q: . Find an orthonormal basis for the subspace of R³ given by {(x, y, z)T : x − y + z = 0}.

A:

Q: A house sells for $165,000 and a 15% down payment is made. A mortgage was secured at 4.7% for 30…

A:

Q: Problem 81. Define the tower function T: NN by the recursion T(0) = 1, T(n + 1) = 2T (n). Thus T(n)…

A: To show that there are infinitely many strings in {0,1}* such that , where is the length of the…

Q: The vectors B= = [x]B= = -{].M]} 8 form a basis. Find a vector x given the B-coordinates of x are

A:

Q: Find a basis {b₁,b2,...} for the eigenspace corresponding to (the eigenvalue) X. -15 -32 -18 12 -56…

A:

Q: Do not use a calculator for this problem. Find the x-value where the relative maximum of y = e ² –…

A:

Q: · y"(t)+5y'(t)+4y(t) = 0, y(0) = 1, y'(0) = 0

A:

Q: A 10-foot ladder leans against the side of a wall forming an angle with the ground. Given that the…

A: Here we use the rate of pull and the angel relationship to the sides of the wall.

Q: Given the following function, list the key features and then sketch a graph. Please upload a picture…

A:

Q: A survey of magazine subscribers placed 61 celebrities in 3 categories. 36 were on the most powerful…

A:

Q: Fill in the blanks in the following proof. Claim: Let xn = 1 + for all n E N. Then x,, does not…

A:

Q: ind an antiderivative G of g(z) z²

A: We have to find the antiderivative of the given function.

Q: Determine whether the given matrix is diagonalizable; if so, find a matrix E and a diagonal matrix D…

A:

Q: Investigators evaluated the effect of education (E1-1 if college or more, E2=1 if Masters degree or…

A: From the question the value of A = 25 and M = 1Since the person only has a college degree we can…

Q: Prove or disprove: Q/Z is isomorphic to Q

A: Group isomorphism

Q: Find the work done by the force field F(x, y) = x sin(y) i + yj on a particle that moves along the…

A:

Q: Use Laplace transforms to solve the integral equation ...... ..... y(t) = 31² - e²² - fy(T)e y…

A: The given integral equation is let  denote the Laplace transform of taking Laplace transform on both…

Q: 4. The generating function for the regular Bessel functions of integer order is [(-)] = [(x). I exp…

A:

Q: < y g(x) A 4 y = f(x) B2 A² D B 2 C D' [C 4 Give an equation for the function y = g(x) in the form…

A: For the given graph of f and g, we see the graphs are similar. The graph of f or g can be achieved…

Q: The graph below is of a function g(x) with domain (-∞0, ∞). It consists of two lines and a…

A:

Q: Given basis = {QOB]} {[ 2 5 3 {C₁, C2, C3}. find the basis C = of R³ and change of basis matrix [B]C…

A:

Q: below is a python code for solving a system of non-homogeneous linear differential equations. Write…

A: The objective of the question is to plot the solution functions h and v obtained from the given…

Q: (a) For which values of p does the integral 1 de converge?

A: Note: As multiple questions have been asked, so only First question (a) have been solved here…

Q: Write the vector v = B - - -3 8 5 -44] 50 24 1 - as a coordinate vector with respect to the basis

A:

Q: Exercise 3.5.101: Describe the behavior of the following systems without solving: a) x' = x + y, y'=…

A:

Q: Compute the work done by the force 7 = (sin(x + y), xy, x²z) in moving an object along the…

A: Given force The object is moving along the straight line and from

Q: In Problem 11 to 15, write each sentence in symbolic form. Represent each simple statement in the…

A:

Q: Consider a function f(x,y)=4x^2+y^2 . Find the minimum value of this function subject to the…

A: The given question is a constrained optimization problem, which can be solved using the method of…

Q: Without​ consultation, each of three organizations announces a​ one-day convention to be held during…

A: