Find the cubic function that models the data in the table below. - 2 - 1 2 3 4 y 36 3 4 6- - 48 y%3D (Simplify your answer. Do not factor. Use integers or decimals for any numbers in the expression. Round to three decimal places as needed.)

Q: Write the equation of the function represented by the parabola in vertex form and in the form y =…

A: Given points vertex (-1,-6)(0,-4)

Q: Given a cubic function with zeros of 1, -2 and 3, and y-intercept of 18, what is the value of the…

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Q: Find the point on the parabola x= - 2t, y = - 2t, - o <t< oo, closest to the point (- 32, – 1).

A: Let the point (x, y)=(-2t, -2t2) on the parabola be the closest point to (-32, -1) So distance…

Q: Find all the hypercritical values of the function. 1 25 f(x) = =a 90x2 12

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Q: Find the sum of the areas of the shaded rectangles under the graph. Round to two decimal places.…

A: Find the heights of the rectangle by the first point of x which is given .

Q: SW 1. Write an equation for the average cost A(x) of printing x sweatshirts through this company.

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Q: Find the angle at which the parabola y=x2−14 intersects the positive x−axis.

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Q: Find a quadratic function that includes the set of values below. (0,7). (2,17), (3,16) ..... The…

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Q: The vertex of the parabola f(r) = a? + 8a + 2 is О (-4, -14) о (-8, -14) О (-12, —14) О (-4,-12) о…

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Q: Q. 3 (b) Fit a Second Degree Equation to the following data. 2 4 8 10 12 Y 10 14 19 25 31 36

A: ANSWER: For the given data,

Q: y varies directly as the cube of x when x=2 then y=11 find y when x=3 enter the exact answer

A: Solution is given as below:

Q: Describe the impact the a-value has on the following function: y = 3(x – 1)2 +1 %3D

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

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Q: Using the graph, determine the coordinates of the roots of the parabola. y 10 8 5 4. 3 1 -10 -9 -8…

A: Roots of the function from the graph

Q: 19. Find the total area between the parabola y = x2 - 4x, the x-axis, and the ordinates x = -2 and x…

A: We can use integration to calculate the area

Q: 25. What are the coordinates of the vertex of the parabola given the function f(x) = x2 + 8x-3 %D

A: f(x) = x2+8x-3 From the above equation we can see that the highest power of y is 1 and x is 2. This…

Q: AP to Suppose that the radius r and volume V = 4Tr³ of a sphere are differentiable functions of t.…

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Q: A. y = x + 3 B. y = 0.5x? – 2 | C. y = 3(x + 2) D. y = -2x + 1

A: We know that the general equation of parabola is , y - k = a ( x - h )2

Q: The roborace is over, but the wonders of math never cease! Does the given graph represent the…

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Q: Q1\ Find the extremals of functionality

A: Given,            Jy=∫x1x2xy'2-yy'+ydx

Q: Solve and draw l Sketch the graph of the pollowing equations: x² + ag? + z - &x t 124 22 + 35 :0 1.…

A: We know that a function in three variables x, y and z is written as z=fx, y or fx, y, z=0, where x,…

Q: An open rectangular box is to be constructed by cutting square corners out of a 18​ by 18​inch piece…

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Q: Find the sum of the areas of the shaded rectangles under the graph. Round to two decimal places.…

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Q: Find the point on the parabola y = (x – 3)² – 5 that is closest to the point (0,0). |

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Q: Sketch the graphs of the following cubic functions, showing x-axis intercepts  a y = −(2 − x)(x +…

A: Since you have asked multiple questions, we will solve the first question for you. If youwant any…

Q: f(t) = (t – 5)² – 9 1) What are the zeros of the function? Write the smaller t first, and the larger…

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Q: Find the point P on the parabola y = x? closest to the point (57, 0). (x, V) = ( y y =x 57

A: Let x, x2 be the point on the parabola y=x2 closest to the point 57, 0. Now the distance between x,…

Q: Sketch the graphs of the following cubic equations onto graph paper. (x) - х' - Зx? -6х +8 b (x) -…

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: 4. Fit a second degree parabola y = a + bx + cx? to the following data 2. 8. 10 y 3.07 12.85 31.47…

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Q: The quadratic function y = ax? + bx + c pass through (2, 1) and tangent to the line y = 2x + 4 at…

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Q: Which of the following is the maximum area for the rectangular which has its two vertices on are the…

A: Consider the vertices lie on the x axis and the coordinates are (x,0) and (-x,0). Also the other two…

Q: Find the point on the parabola * +y“ that is closest to the point (0, -3). =

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Q: Find the point on the parabola (y = x2/2) that is closest to the point (-4,1)

A: Use distance formula to evaluate

Q: A rectangle has its base on the x-axis and its upper two vertices on the parabola y=6-x² What is the…

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Q: Find the point on the parabola y 2 =2x that is closest to the  point ( 1, 4)

A: Given: y2=2x let's point on parabola is t22,t now, if point1,4 is closest to t22,t2 then product of…

Q: On a given day, the flow rate F (in cars per hour) on a congested roadway is given by the equation…

A: Given that  F=V/(22+0.03V^2) To fidn the speed will maximize the flow rate

Q: The graph below shows the relationship between the height of the water in a bottle (in inches), h,…

A: From the graph we can see that  when the height of the water in the bottle is 0.5  then the volume…

Q: Use the exponential definitions of hyperbolic functions to find the values of A and B if: 5e' -4e =…

A: We have sinh(t) =et-e-t2cosh(t) =et+e-t2

Q: Find a quadratic function that includes the set of values below (0,3). (2,13), (4,7) ...... The…

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Q: Find an expression for a cubic function f if: a. ?(0) = ?(1) = 0 b. ?(−1) = −10 c. ?(2) = −22

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Q: ind the vertex and the x-intercepts (if any) of the parabola. (If an answer does not exist, enter…

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Q: 52² – 5y? lim (2.)(0,0) 7x2 + 7y

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Q: Find the area of the enclosed by the parabola y=x2-8x+15 and the x-axis .

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Q: Find the cubic function that is the best fit for the data in the table below.

A: To find  :                   The cubic function.       f(x) = 2.970 x3 - 3.3600 x2 - 3.7000 x +…

Q: The area of the region below the parabola y = 9- x² and above the x-axis is a. 12 b. 24 с. 36 d. 48…

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Q: 10. Fit a second degree parabola to the following data. 3 4 Y 1090 1220 1390 1625 1915

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Q: D = R = Function?

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Q: In our modern era, digital television is a norm, and most homes have HDTVs. HDTVs are usually…

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Q: Use either a graphing calculator or a spreadsheet to complete the table. Express all your answers as…

A: In each cases Substitute the values of x and y than simplify.

Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is the intersection point of the main axis. In an ellipse graph, the center of the axis is the midpoint of the line segment connecting the foci. The major axis is the line section that runs through the ellipse's foci, while the minor axis runs through the middle and is perpendicular to the major axis.. The ellipse has two endpoints on the major axis which are known as the vertices (in plural), vertex in the singular. The equation of the major axis is 2a, the equation of the minor is 2b and the distance between the major axis and minor axis is 2c. The semi-major axis has a length of a and the semi-minor axis has a length of b. The ellipse's vertices are determined by the elliptical orbit's equation and graph.