8. Find the best parabola to fit the data points: (-1, –1), (0, 1), (1,0), (2, 3).

Q: Find the equation of the parabola and put it in the form f(x)= ax^2 +bx+c  Given:  Vertex: (2/3 ,…

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Q: Find the parabola with equation y=x^2+bx+c that has slope of 8 when x=9 and passes through the…

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Q: Find the coordinates of the vertex of the parabola y = x^2 - 4x + 1 using derivatives O (2, -3) O…

A: To find the vertex of the parabola by using derivatives

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

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Q: At what point does the line normal to the graph of y=5−4x+4x2 at (1,5) intersect the parabola a…

A: The given function is- y=5-4x+4x2.................1 Differentiating the above expression w.r.t. x-…

Q: There is a parabola which has a minimum where the two lines 3x+6y-1=0 and 2x+ y-2=0 intersect. The…

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Q: Find the dimensions of the rectangle of largest area that has its base on the x-axis and its other…

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Q: Find the dimensions of the rectangle of largest area that has its base on the x-axis and its other…

A: Draw the parabola y=7-x^2.

Q: How many common points does the parabola y=x2-2x-2 have with the straight line a) y=2x-6; b) x-…

A: Solving two equations

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: Suppose you are given the x-coordinate of a point on a parabola. How can you find the matching…

A: According to Bartleby guidelines, only one question can be solved at a time. Kindly post other…

Q: Find the dimensions of the rectangle of largest area that has its base on the x-axis and its other…

A: Topic = Application of Derivative

Q: 3. Find the natural cubic splines that pass through the given data points. 3 4 6 y 10 15 35

A: The natural cubic splines that pass through the given data points, Then the cubic spline fx is such…

Q: Any point on the parabola can be labeled (x, y), as shown. 4 3 2 (*, y) ¢ -6 -5 -4 -3 2 - 1 2 3 4 5…

A: According to figure equation of parabola in standered form X2=4bYnew equation of…

Q: Suppose that a random parabola has a minimum vertex at (6,5) what would be the value of the axis of…

A: The axis of symmetry for a parabola is the line about which the parabola is symmetrical. The…

Q: Identify the x-intercept(s) of this parabola. 10 8- 6- 4- -6 -2 2. 6 -4 O (3. 0)

A: x-intercept is the point where the graph crosses the x-axis.

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: Find the equation of the plane perpendicular to the y-axis and passing through the point (3,2,-2)

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Q: Find a parabola with equation y= ax2 + bx +c that hasslope 4 at x=1  , slope -8 at x= -1 , and…

A: The parabola is y=ax2+bx+c. It has a slope of 4 at x=1 and slope of -8 at x=-1 and passes through…

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: 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: Consider a parabola that intersects the x-axis at points (-1, 0) and (3, 0).

A: We need to find an equation of parabola that intersects the x-axis at (-1, 0) and (3, 0). Thus,…

Q: What point on the parabola y=(6−x)2 is closest to the point (6​,6​)?

A:

Q: Determine what is the minimum distance from the origin to the line  y=-2x+5

A: topic - distance of line from origin

Q: 3. Find the best parabola to fit the data points: (-1,1), (1, –1), (2,0), (3,0).

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Q: Find the best parabola to fit the data points: (-1,1), (1, –1), (2,0), (3,0).

A: The given points are (-1,1),(1,-1),(2,0),(3,0).

Q: Find the point(s) of intersection of the parabola with equation y = x2 - 5x + 4 and the line with…

A: Given equations are,

Q: Find the equation of a parabola that has a vertex of (-2, -1) and contains the point (0, 3).…

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Q: Determine the points of intersection of the parabola y=2x^2 +12x +10 and the line y=4x+2

A: I am attaching image so that you understand each and every step.

Q: (3) Find the coordinates of the points of intersection of the parabola y = x2 - ax and the line y =…

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Q: For the given data (0, 1), (1, 1), (2, 3), (3, 5) find the line y = ao + a1x that best fits the data…

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Q: Find the minimum distance from the point (4, 2) to the parabola y² = 8x. A 4/3 (B 2/2 /3 D 2/3

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Q: 2 What are the intersection points of the parabola given by the equation y = x“ – 9 and the line…

A: We are answering only the first question as per our honor code. Given, The equation of a parabola…

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: 2. A parabola with axis parallel to the x-axis and passing through (5,4), (11, –2) and (21, –4)

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

Q: What point on the parabola y = 3- x² is closest to the point (3,3)? The point on the parabola y = 3…

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Q: What point on the parabola y = 6 – x is closest to the point (6,6)?

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Q: 7. Write an equation for each parabola a) 0, 11) 8- 4- (4, –5) b) | YA |(-6, 4) 4- (-5.3) 2 -6 -2 0…

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Q: What point on the parabola y = 5-x is closest to the point (5,5)? The point on the parabola y = 5- x…

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Q: 2. Suppose that the graph of y = ax²+bx+c is a parabola which vertex is V (-3, 7), what is the…

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Q: How many common points does the parabola y=x2-2x-2 have with the straight line a) y=2x-6; b) x-2y=4?

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Q: Find the shortest distance of the point (10,4) to the parabola y=x2

A: Consider a  point on parabola  y=x2. Distance of this point with (10,4) s2=(x-10)2+(y-4)2…

Q: Find the x-intercept(s) and the coordinates of the yertex for the parabola y =x´ +4x+4. If there is…

A: The given parabola is: y=x2+4x+4 To find the x-intercept and the coordinate of the vertex for the…

Q: Find the shortest distance of the point (6,3) to the parabola y=x2

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Q: Find the equation of the parabola y = ax^2 + bx +c that passes through the points (-1,-4) (1,4), and…

A: topic  -  parabola

Q: Find the equation of the line tangent to (a) The parabola z = 2x² - 3y², y = 1 at the point (-2,1,5)…

A: Given: we have to find equation of tangent lines   equation of tangent line : y-y1=m(x-x1)

Q: Determine the coefficients a, b, and c of the parabola y = ax² + bx +c that passes through the point…

A: Solution is here

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.