Find a parabola with equation  y = ax2 + bx + c  that has slope  13  at x = 1, slope  −19  at x = −1, and passes through the point  (2, 33).

Q: At what point of the parabola is the tangent line parallel to 7x+y-2=0? y=2x^2-3x+1

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Q: What is the maximum vertical distance between the line y = x + 30 and the parabola y = x2 for -5 s x…

A: given, equation of line is y = x + 30 and equation of parabola is  we have to find maximum vertical…

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 equation for the curve in the xy-plane that passes through the point (1, -1) if its slope…

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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: 2. Find y in terms of x if = 6x² – 2x and the curve passes through the point (1, 5). -

A: We have to find the value of x if dydx=6x2-2x and the curve passes through the point (1,5).…

Q: Show that the x-coordinate of the vertex of the parabola whose equation is y = ax2 + bx + c occurs…

A: Given the equation of a parabola y=ax2+bx+c

Q: Hello. Can you please explain this problem to me?

A: Slope of the function is the derivative of the function.

Q: A parabola has the equation y^2 = -4ax. Determine the slope of the orthogonal trajectories.

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Q: Find a parabola with equation y = ax2 + bx + c that has slope 11 at x = 1, slope -25 at x = -1, and…

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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 equations of both lines through the point (2, –3) that are tangent to the parabola y = x2 + x.

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Q: The slope of the tangent line to the parabola y = 2x + 5x + 7 at the point (- 4, 19) is: The…

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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…

A: To find a parabola with equation.

Q: The slope of the tangent line to the parabola y= 4x2 + 2x + 4 at the point (-1, 6) is : ?  the…

A: Consider the equation of the parabola, y=4x2+2x+4 The first derivative dydx of the curve at any…

Q: Does the parabola y = 2x-9x+4 have a tangent whose slope is - 1? If so, find an equation for the…

A: Given Parabola, y = 2x2 - 9x + 4

Q: Find a parabola with equation y = ax² + bx + c that has slope 4 at x = 1, slope -16 at x = -1, and…

A: We know slope of a curve y=f(x) is given by, dydx=f'(x)

Q: Use the derivative to find the vertex of parabola. y = -2x2 + 12x - 5

A: Given equation of parabola is y=-2x2+12x-5. To find the vertex using derivative. Solution: We know…

Q: Find equations of both lines through the point (2, - 3) that are tangent to the parabola y = x2  + x…

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Q: The slope of the tangent line to the parabola y = 4x? + 7x + 2 at the point (– 4, 38) is: The…

A: Equation of parabola,  y = 4x2 + 7x + 2 Given point is (-4, 38)

Q: Find the point on the curve y = /2x + 3 which is closest to the point (5, 0).

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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: Find the equations of the tangent lines to the parabola y = -x² + 5x – 6 at its points of…

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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: Find the curve y = ƒ(x) in the xy-plane that passes through the point (9, 4) and whose slope at each…

A: Given, the curve y = ƒ(x) in the xy-plane that passes through thepoint (9, 4) and whose slope at…

Q: The slope of the tangent line to the parabola y 3x2 + 2x + 6 at the point (5, 91) is: The equation…

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Q: Find the slope of the curve at the given point: y = x(4x − 1)², (1, ²) -

A: Given query is to find the slope of the curve at given point.

Q: Find the equation of the curve that passes through the point (3, 2) if its slope is given by y = dy…

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Q: What is the maximum vertical distance between the line  y = x + 12  and the parabola  y = x2 for…

A: See the attachment

Q: Find an equation of the parabola y = ax2 + bx + c that passes through (0,1) and is tangent to the…

A: Since, the parabola passes through (0,1) ,so,we substitute x=0, y=1 ,to get c=1

Q: Find equations of both lines through the point (2, −3) that are tangent to the parabola y = x2 + x.

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Q: Find equations for two lines through the origin that are tangent to the ellipse x2 – 8x + y² + 3 =…

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Q: Find an equation of the curve that passes through the point (0, 2), and has the given slope y′ =…

A: y'=x4y, (0,2) Formula ∫xndx=xn+1n+1+C

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 member of the curve whose slope at any point is 2e** and passes through the point (0, 1)

A: We need to find the member of the curve whose slope at any point is 2e^(4x) and passes through…

Q: Find the equation of the tangent line to the parabola at the given point. x2 = 2y,  (−9,81/2)

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

A: y'=-9x16yPasses through (1,1)Formula∫xndx=xn+1n+1+C

Q: The slope of the tangent line to the parabola y 4x? + 7x + 3 at the point (0, 3) is: The equation of…

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Q: The slope of the tangent line to the parabola y 3x? + 2x + 3 at the point (– 5, 68) is: The equation…

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Q: Draw a diagram showing two perpendicular lines that intersecton the -axis and are both tangent to…

A: The given parabola equation , y=x2. To draw two perpendicular lines that intersect on the axis and…

Q: Find x for which the line tangent to the parabola y = 4x − x^2 is horizontal

A: The objective is to find x for which the line tangent to the parabola y = 4x − x^2 is horizontal.

Q: The slope of the curve y=x' +3x² – 6x +5 at (1,3) is -

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Q: Find the equation of the line tangent to the ellipse x^2 - xy + 2y^2 - 4x + 2y + 2 = 0 if the…

A: given equation of ellipse x2-xy+2y2-4x+2y+2=0 and a line  4y-x+2=0 to find equation of line tangent…

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: Find an equation of the curve that passes through the point (0, 4) and whose slope at (x, y) is x/y.

A: Solution:find the equation of curuepasses through the point (0,4)slope of cwue is xydydx=xyy dy=x…

Q: Q3// Does the parabola y = 2x2 13x + 5 have a tangent whose slope is (-1)? %3D If so, find tangent…

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Q: Find the equation of the line tangent to the parabola y = x^2 -1 at the point (-2,3).

A: Given the parabola :

Q: Find an equation of the curve that passes through thepoint (0, 1)and whose slope at (x, y) is xy.

A: To Determine: Find an equation of the curve that passes through the point (0, 1)and whose slope at…

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…