A quadratic function is of the formf(X) = ax-+ bx + c and when we set f(x), or y, equal to zero we call it a quadratic equationax + bx +c = 0. When we set y equal to zero and solve for x we are finding the x- intercepts. Here are three quadratic equations: y = x2- 2x – 1 y = - 3x²+12x – 12 y = x2-6x + 13 Using your graphing calculator find the x-intercepts, y-intercepts, and the maximum or minimum values of the quadratic equations. • Confirm your answers using the Quadratic Formula program. • Last, since your calculator only gives real number approximate answers for the zeroes solve these by hand to provide us with exact answers (might be complex numbers).

Q: Find the value of b and c in the form x2 + bx + c = 0 with solution x = 2- V3 and %3D x=2+ 3.

A: b= -(sum of solution)  c= product of solution

Q: hat is the average of the two solutions of the abitrary quadratice equation ax2 + bx +c = 0

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Q: Use the method of undetermined coefficients to determine the form of a particular solution for the…

A: We have to find ypx, particular solution for the given differential equation      y'''+y''-2y=xex+5…

Q: (b) To find the daily optimum production number of Portland cement in a factory, one needs to solve…

A: The Gauss Seidel method is an iterative technique used to find the approximation of the solution of…

Q: 4. Find the value(s) of b in the quadratic equation x² + bx + 1 = 0 such that it has one solution.

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Q: For the quadratic equation ax2 + bx + c = 0, the discriminant is D = The discrimin If D> 0, the…

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Q: Solve the particular solution (D2+3D+5)y = 5e-xsin2x using  D- operator method.

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Q: Find all solutions of the equation x2y' = y3 − 5x2y3 explicitly

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Q: Find the solution to the equation 4x2 + 5x = 2x + 2 -3± y38 -7± y17 8 X = X = 8 а. -3± V41 X = 8. С.…

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Q: x  -  2y  +3z  =17 2x  +  y   +z =  9 -3x  +2y  - 2z  = -19   solve for x,y,z

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Q: Find the general and particular solution of the y"=3e³x if f(2)= k and f'(2)=k²

A: y"=3e³x if f(2)= k and f'(2)=k²

Q: Any solution of the linear equatioon 2x + 0y + 9 =0  in two variables is of the form

A: The Given equation is: 2x+0y+9=0

Q: Find the particular and general solution of y'''-3y''-10y'+24y=48e-2x  using Variation of parameters

A: Given, y'''-3y''-10y'+24y=48e-2x Complementary solution of the homogeneous equation is given by…

Q: Determine the r- and y-intercepts for h(x) = 6x – 42. Solve -7x – 8y = 1 for y.

A: Given: (a) h(x)=6x-42(b) -7x-8y=1

Q: 2x1-x-4x₁x₂ = 0 -x + 2x3-4x₁x₂ +10x₁ = 5

A: We need to solve the following system of equations using a numerical method.…

Q: Q2/ A/ Find the equation of straight line passing through the point (1, 2) and parallel to the line…

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Q: The concentration of a drug in the bloodstream C(t) at any time t, and hours, is described by the…

A: The concentration of drug reaches its maximum when                         C'(t) = 0find the values…

Q: [1] Solve for the GS of (D4-5D³+9D²-7D+2)y=0

A: By Bartleby policy I have to solve only first one as these are unrelated problems.These are…

Q: Q5) by using the (graphical method) find the optimum solution of X1, X2 that the maximum Z=4X1+5X2…

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Q: Use the method of undetermined coefficients to solve y''- 4y'+3y = x^2+ 2x-3e^3x.

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Q: Solve for the general solution of (D: - 5D + 6)y = 4e* using method of undetermined coefficients.

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Q: Solve * + 3x - 4x = 20t, given that at t = 0,x = 0 and i = 0.

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Q: Obtain the general solution. (D^2- 2D + 2)y = 0

A: Using solution of Linear Differential Equations with constant coefficients.

Q: Find a general solution of y" (-2-2 i3)y. y(x) =

A: The given differential equation is  y'' = (- 2 - 2i√3)y or, y'' - (- 2 - 2i√3) = 0 or, (D2 + 2 +…

Q: Q1: Find the general solution of the y - 4y - 5y = 2sin2 x

A: Given differential equation is y''−4y'−5y=2sin2x. We have to find the general solution of the given…

Q: H4. Use the method of variation of parameters to find the general solution of dy -X- - 3y= 4x³. dr2

A: Please find attachment for the details solution

Q: 3. Find all solutions to the equation (D² + 1)²D² f(x) = 0.

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Q: The profit from the sale of x units of radiators for automobiles and y units of radiators for…

A: Consider the profit function: Px,y=-x2-y2+4x+10y Given constrains are, x≥0y≥0x+y≥7 Now convert these…

Q: Q1// Solve by Graphics the mathematical model Маx Z %3D Зx1+ 2x2 s.t -x1 + 2x2 S4 3x1 + 2x2 s 14 х1-…

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Q: C. Solve by the method of elimination. 1. Зу 2x + 3y =13 =D2 2. 3x + 10y = 2 X- 2y = - 6 3. 3x+ 2y =…

A: The elimination method is used to find the solution of algebraic equations. In the elimination…

Q: A popular three-story dollhouse has a price-demand equation given by p=D(x)=207-0.8x and the…

A: The demand equation is: p=207-0.8x The supply equation is: p=0.2x+132

Q: Find the solution to the Bernoulli Equation. 2x³y = y(y²+3x²)

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Q: (a) To find where the graphs of the functions y = m¡x + b1 and y = m2x + b2 intersect, we solve for…

A: a) To find where the graphs of the functions intersect, we solve for x in the equation:…

Q: Find a particular equation for the DE: y+4y'-2y= 2x -3x+6

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Q: Solve the quadratic for x: f (x) = (3x – 6) (4x + 12) Ox= 6 and x = -12 Ox = -2 añd x = 3 Ox = 2 and…

A: We have to solve the quadratic equation: fx=3x-64x+12 To solve the given equation we need to put…

Q: Find a quadratic equation of the form ax² + bx +c = 0 whose solutions are x = 4±V1I. %3D

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Q: 2 4. The function y = x² +10x+25 the y-intercept is (0,25) 5. The only root of the equation 2x²+x=0…

A: Given :4. y=x2+10x+255. Root of the equation : 2x2+x=0

Q: Find all real solutions. (a) x - x - 12 = 0 (b) 2x2 + 4x +1 = 0 (c) 3 – Vx – 3 = x (f) 3|x - 4 = 10…

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub-  parts for…

Q: y"-y-4e-x+3e2x; y(0) - 0.y(0) --1.y"(0)-2

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Q: Solve using any method. -x- 2y = - 13 - 4x+ 2y=2 A inconsistent

A: Given equation  -x-2y=-13      (1) -4x+2y=2          (2)

Q: 1. a) Identify the following equations as linear, quadratic or neither. i) y = -x? - 4x + 2 ii) y =…

A: We are authorized to answer three subparts at a time, since you have not mentioned which part you…

Q: Find the general solution of the x²y" + xy' − y = 3x, x‡0;

A: *By Bartleby policy I have to solve only first one as these are all unrelated problems.These are all…

Q: Find the general solution (D3-3D2-3D+1)y = 0

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Q: (b) Show that for x > 0 and k + 0 the equations In x x* = e* and 1 have the same solutions

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Q: Use the method of undetermined coefficients to determine the form of a particular solution for the…

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Q: 10. Solve for x and y: 3x - 5y = 13 -2х - Зу %3D 4

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Q: Find the particular solution of (2x + 3)y = y + (2x + 3)/2; when x = -1, y = 0 Show your solutions…

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Q: Find the general solution of: x² = y² QY_ dr

A: We have to find general solution of given differential equation.

Q: Solve the pollowing vyrtemr of equationN uring matricar a. ex tytz =4 X-24 +32=7 -3x tây-22=-10

A: We will answer the first question as we don't answer multiple questions at a time. Please resubmit…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.