8. Find the function that will generate the points on a parabola that opens down, has a base of 4 meters, and a height of 6 meters: -4a(y– k) = (x – h)²

Q: Find a parabola with equation y = ax2 + bx + c that has slope 8 at x = 1, slope −12 at x = −1, and…

A:

Q: Determine the general equation of a parabola opening downwards whose vertex is at (3,-4) with a…

A:

Q: Find the maximum and minimum values of the function f(x, y) = xy on the ellipse given y? by the…

A: According to the given information, it is required to find the maximum and minimum value of the…

Q: 7. Determine all values of a that will cause the parabola y=ax² +10x+1 to cross the x-axis at two…

A: 7) y=ax2+10x+1 ...................eq (1) For parabola to cross the x- axis put y=0 0=ax2+10x+1…

Q: ,2 The vertex of the parabola of f(x)=x²+x is

A: Equation of the parabola :y=a(x-h)2+kwhere (h,k) = vertex of the parabola

Q: Suppose that the Celsius temperature at the point (x, y, z) on the sphere x² + y² + z² = 1 is…

A: Let's find lowest and highest temperature by using langrange multipliers.

Q: 3) Fit a parabola to the data. X 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 y 3.1950 3.2299 3.2532 3.2611…

A: The equation of a parabola is y=a+bx+cx2. The method of least square can be used to obtain the best…

Q: Find the asymptotes of the cissoid of Diocles defined by the equationy2(2a−x)=x3,a>0.

A:

Q: 13. The parabola y = x2 + x + 1 opens: A. To the right %3D B. To the left C. Upward D. Downwarč

A: y=x2+x+1 here parabola is in the form of y=ax2+bx+c which means it can be open up or down…

Q: Show that line d:3x-4y-5=0 is tangent to hyperbola H:x2-4y2=5 and find the point of contact of the…

A:

Q: 2. What is the value of y anytime a parabola intersects the x-axis?

A: It is known that the value of y on x-axis is always 0.

Q: Write the general solution of the fourth-order DE y(4) – 2y" + y = 0 entirely in terms of hyperbolic…

A: We have to find the general solution of the differential equation y4-2y''+y=0. The auxiliary…

Q: Find the maximum and minimum values of the function f(x, y) = xy on the ellipse given. y? by the…

A:

Q: write a cubic function y=ax^3+bx^2+cx+d that has a local maximum at (4,0) and passes through (1,-1)

A: Consider the cubic function: y=ax3+bx2+cx+d…

Q: Find the asymptodes of Hx)= x²- 5x+6 the funchion given below X-2

A:

Q: The orthogonal trajectories to the family of hyperbolas xy= C is given by the family 1)y=cx 2)y2 -x2…

A: We need to find the orthogonal trajectory to the family of hyperbola xy=c

Q: e. Find points on the graph of xy°z² = 16 that are closest to the origin.

A: Let P be point (x0,y0,z0) Then, distance between P and origin is given by

Q: Show that the number 4p is the width of the parabola x2 = 4py (p>0) at the focus by showing that…

A:

Q: Find the best quadratic approximation, Q(x, y) of V9 – 6x – 4y for (r, y) near (0,0).

A: We have to find the best quadratic approximation Q(x,y) for (x,y) near (0,0).

Q: Find constants a and b so that the minimum for the parabola f(x) = x2 + ax + b Occurs at the point…

A: The given parabola is : f(x)=x2+ax+b We need to find the values of a and b so that the minimum for…

Q: 9) Find the point on the parabola y = 10-x² closest to the point (0, 5.5).

A: Given question:- Find the point on parabola y= 10-x2 closest to point (0,5.5)

Q: Please confirm if the selected answer is correct ?

A:

Q: Find the minimum distance from the point (4,2) to the parabola y2 = 8x.

A: We have to find the minimum distance from the point (4,2) to the parabola y2=8x.

Q: The Gateway Arch in St. Louis was designed by Eero Saarinen and was constructed using the equation…

A:

Q: (ii) Find the extremum of Z= x2 +y2 subject to x + 4y 2 and examine whether the %3D %3D stationary…

A:

Q: 2. Write the general equation of the parabola with directrix at x FG,-1), and v (. -1). 2

A:

Q: 13. Find the point on the parabola y* = 2x that is nearest the point (1, 4). %3D

A: As per our guidelines we can solve only one question or three sub-parts. To ask more please…

Q: Figure 4.6 shows the curves y = Vx, x= 9, y = 0, and a rectangle with its sides parallel to the axes…

A:

Q: - Find a parabola with equation y = ax? + bx +c that has slope 4 at x = 1, slope –8 at x = -1, and…

A:

Q: Show the complete solutions. Family of horizontal parabolas whose h to k ratio is 2. Ans: 2xy" -…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Given f(x, y) = x² – 4y, the parabola x - 4y = 8 = 0 is the level curve o -8 None of the given…

A: The solution is given below

Q: write a cubic function y=ax^3+bx^2+cx+d that has a local maximum value of 3 at -2 and a local…

A: Definition used -                 The maximum and minimum value of a function -…

Q: Find the coordinates of the vertex for the parabola defined by the given quadratic function. 2(x -…

A:

Q: Find the length of the parabola given by c(t) = (t, t2) for 0 ≤ t ≤ 1.

A:

Q: Find a parabola with equation y=ax^2+bx+c that has slope 4 at x = 1, slope -8 at x = -1, and passes…

A:

Q: The parabola y + 2y + 8x –7=0 has vertex at O (-1, –1) o (-1,1) о (1,-1) о (1,1)

A:

Q: Given f(x, y) = x² - 4y, the parabola x² - 4y - 2 = 0 is the level curve of fat 02 0-2 01 00 None of…

A: Ggg

Q: 4) Find the orthogonal trajectories of the family of parabolas y – 3 = c(x + 1)².

A:

Q: 3- The parabola y= ax'+bx+c, mean that the cquation y = ax is .........

A: As this is a multiple question according to the Bartleby Answering rule, only first question is to…

Q: The tangent and the normal to the parabola y²=20x at the point T(5,10) meet the x-axis at the points…

A: Details solution is given below:

Q: 1. Give the (x, y) coordinates of the vertex of the parabola y= x - 2.x + 5, and indicate whether it…

A:

Q: 1. Find the point on the parabola y = 3 – x² that is closest to the point (6, 0).

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Q: The a value in the function f(x) = 2x2 makes the parabola %3D O more wider moves it left

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Q: I For the parabola -2x = 16y + 4y² + 13, for what value of y does x have a minimum? 3. If the

A:

Q: Compute y ds over the part of the parabola y =2Px, for P > 0 starting at (0,0) at (2P,2P).

A:

Q: 19 Find the minimum value of the parabola y = x – 8x +

A: The minimum value of the parabola or any curve is obtained where y' = 0

Q: 33) Find the points of intersection between the line x - y - 2 = 0 and the parabola y = 4 - x 2.

A:

Q: 16. Evaluate (x + V9) ds where C consists of two segments: the part of the parabola y = x² from…

A: In the given question we have to evaluate the integral ∫C(x+y)ds where C is the regionconsist of two…

Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.