Graph the given parabola by determining the vertices and using first derivative test y = 3x4- 8x + 6x² www

Q: What point on the parabola y=3−x2 is closest to the point ​(3​,3​)?

A: Basic differentiation is required.

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: Finally, determine a. The parabola passes through the point (0, 5). Substitute the values of x and y…

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Q: Find the equation of the tangent line to the parabola at the given point. x2 = 2y, (-5, ) 2у, %3D

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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: Q3// Does the parabola y = 2x2 - 13x + 5 have a tangent whose slope is (-1)? If so, find tangent and…

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Q: What is the most time-consuming part in using a graphing utility to graph a general second-degree…

A: To discuss about graphing utility.

Q: Find equations of both lines through the point (2, −30) that are tangent to the parabola y = x^2 -…

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Q: Find a parabola with equation  y = ax2 + bx + c  that has slope  13  at x = 1, slope  −19  at x =…

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Q: A parabola of y=x^2 has been regraphed and now sits with each side plotted at (-3,5) and (3,5) and…

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Q: Find an equation of the curve that passes through the point (1, 3), and has the given slope y′ =…

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Q: What is the families of the curve of all Parabolas with symmetric axis parallel to the y-axis and…

A: Given: What is the families of the curve of all Parabolas with symmetric axis parallel to the y-axis…

Q: Show the complete solutions. Family of horizontal parabolas whose h to k ratio is 2.

A: Let's find differential equation.

Q: <, y) = )-« lustrate with a sketch. y 4 3 3 2 2 2 1 -4 -3 -2 1 1 2 4 -4 -3 -2 4 -4 -3 -2 /1 -1 -2 -3…

A: Topic:- calculus

Q: Find the orthogonal trajectories for the family of curves 3x2 − y2 = C. Use a graphing utility to…

A: Given:  The family of curves: 3x2 − y2 = C

Q: 2. f(x) = 2 - 5x + 2x Sketch: Opens: Vertex: Equation for Axis of Symmetry:

A: The quadratic function is f(x)=2-5x+2x2 Let the function of the form f(x)=ax2+bx+c, if a &gt; 0 then…

Q: Find an equation of the tangent line to the parabola y = x2at the point (2, 4).

A: To find the equation of the tangent line to the parabola y = x2at the point (2, 4). For the parabola…

Q: Find an equation of the curve that passes through the point (3, 1), and has the given slope y′ = −…

A: Given that y'=-y5xdydx=-y5x

Q: Which point on the graph of the parabola y 4x has the minimum distance between the graph and the…

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Q: Find the point on the curve 4x

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Q: Find the vertex of the given parabola. Give all values correct to 3 decimal places. y = 7x2 - 8x +…

A: A detailed solution is given below

Q: Find a parabola with equation y = ax2 + bx + c that has slope 5 at x = 1, slope −11 at x = −1, and…

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Q: Give 3 points that lie on the parabola y=x^2-5x-2

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Q: Find the orthogonal trajectories for the family of curves y2 = Cx3 . Use a graphing utility to graph…

A: Given curve is y2=Cx3.

Q: 1 ,-8 5) /17 - V17 1- v17 1- V17 y = 2(x + 2 y = 2x 2 2

A: Given :           The vertex of parabola is V12, -812.  To find the equation of a parabola which…

Q: What is the equation of parabola in standard form whose focus is at (-4,0) and the directrix is at…

A: Note that, the equation of the parabola with the directrix x+a=0 and the focus (a,0) is y2=4ax.

Q: Find an equation of the tangent line to the parabola at the given point. y = –4x2,  (9, –324)

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Q: Find the equation of the line normal to the parabola y = x2 - 6x + 12 perpendicular to the line that…

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Q: 2. Find the coordinates of the midpoint between the two points on the graph.

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Q: The slope of the tangent line to the parabola y 2x2 + 2x + 4 at the point (0, 4) = The equation of…

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Q: The point (0, 1) has the distance from the line defined by y = -2x – 1

A: Solve for distance

Q: Does the parabola y = 2x2 – 13x + 5 have a tangent whose slope is (-1)? If so, find tangent and…

A: Given:  The equation of a parabola y=2x2-13x+5. We have to find whether the parabola have a tangent…

Q: Find the slope of the tangent line to the parabola y = x2 at the point (2, 4) by analyzing the…

A: We have to find the slope of tangent line to the given parabola y=x2 at the point 2, 4 by analyzing…

Q: The slope of the tangent line to the parabola y = 3x + 3 + 4 at the point (5, 94) is: 33 The…

A: Equation of parabola y=3x2+3x+4 The slope of the parabola at any point is calculated as  dydx=6x+3…

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 an equation of the curve that passes through the point (1, −2), and has the given slope y′ =…

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

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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: Find the equation of a parabola that has a vertex of (2, -4) and contains the point (1, -7).…

A: Given  Vertex of parabola (2,-4)  And contains the points (1,-7)

Q: The slope of the tangent line to the parabola y 3x + 3x +7 at the point (- 5, 67) is: The equation…

A: Take the derivative and put the given point.

Q: What point on the parabola y = 1-x is closest to the point (1,1)? The point on the parabola y = 1-x2…

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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: 3// Does the parabola y = 2x2 – 13x + 5 have a tangent whose slope If so, find tangent and normal…

A: Q3    y = 2x2-13x+5 -*      dydx=4x-13if scope of the tangent be -1 thendydx=-1 as than paint of…

Q: What is the families of the curve of all Parabolas with axis parallel to the x-axis

A: The equation of a parabola with vertex at (h,k) latus rectum equal to 4a and axis parallel to X axis…

Q: Suppose the axis of a parabola is parallel to the yy-axis and passing through the points (0,3),…

A: Given that, the axis of a parabola is parallel to the y-axis. Let the Vertex of the parabola (h, k)…

Q: Use the derivative to find the vertex of the parabola. y= -2x-8x +4 ..... The vertex is (Type an…

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Q: What is the average distancebetween the parabola y = 30x(20 - x) and the x-axis on theinterval [0,…

A: The equation of parabola is given by y=30x20-x on [0, 20] The expression to evaluate the average of…

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.