Find the equation of a parabola with vertex on the line y = 2X, axis parallel to the x- axis and passing through (, 1) a |and (3, 4).

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

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

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 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 the standard equation of the parabola with x intercepts at x = 2 and x -3, and a y-intercept at…

A: Solution is given below

Q: What is the equation of the line tangent to the parabola y2=12x at point (2,2)

A: y2=12x  ⇒  4a=12                     a=3

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 formula for a parabola with its vertex at (9,4) and with a second derivative of -3. f(x)=

A: let's equation of parabola is given by y=ax2+bx+c                                              ..1…

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: In the xy-plane, a line that has the equation y = c for some constant c intersects a parabola at…

A: in the xy-plane a line that has the equation y=c for some constant c intersects a parabola at…

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: 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: 13. Write the equation of the parabola with x- intercepts at ( 3,0) and (9,0) that passes through…

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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: Topic = Application of Derivative

Q: # 3) Create the equation of the cubic, in standard form, that has x-intercepts of 3, -1, and 2…

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Q: Find equations of both lines through the point (5, –6) that are tangent to the parabola y = x2 – 3x

A: topic - equation of tangent to curve

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

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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: Which is the equation of a parabola that has x-intercepts at (2,0) and (-6, 0)?

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Q: The slope of the tangent line to the parabola y=4x2+2x+6y=4x2+2x+6 at the point (-3,36) is: ?

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

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

A: Given equations are,

Q: The line y = 2x - 9 is tangent to the parabola y = x'2 + ax + b at the point (4,-1). What are the…

A: Given y=2x-9 is tangent to y=x2+ax+b at (4,-1) So, y=x2+ax+b passes through (4,-1)Put x=4 and…

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: find the general equation of the parabola with horizontal axis which crosses the x-axis at x=2 and…

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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: Find the point on the line y = 2x + 1 that is closest to the point (2, 2).

A: Given: Given equation of the line is y=2x+1 We want to find the point on the line  y=2x+1 that is…

Q: . Find the equation of the parabola with x-intercepts -7 and 3, and that 2, -11). Express your…

A: Given parabola has two x-intercepts, (-7, 0) and (3, 0). Clearly its either upward or downward…

Q: Find the standard form for the equation of the line which passes through the point (5, –19) and…

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Q: Find the points of intersection of the parabola with equation 2x + y² + 4y – 2 = 0 and the line…

A: Here we find the intersecting point of parabola and the line.

Q: ress 3x² + y² + 2z² + 6x – 4y

A: Given,            3x2+y2+2z2+6x-4y-12z+26=0

Q: Find the equations of the curve for which y" = 6x2  and which passes through the points (0,2) and…

A: We have to find equation of curve, With differential equation y" = 6x2  which passes through the…

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: 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 graph of y = 4x'-9x-7 at the point (1,8).

A: Method to find tangent at a point of any curve.

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: 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: 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: Find the equation of the family of curves whose slope at any point (x, y) is 2. y 4. equal to the…

A: We need to find the family of curves. NOTE - As per our guidelines we can not solve multiple…

Q: Find an equation of the parabola that is symmetric about x-axis, has its vertex at the origin and…

A: Since we know that standard equation of the parabola that is symmetric about the x-axis and has…

Q: Find the equation of the line parallel to the line y= 4x+3 and passes through the point (0,2)

A: This question is based on equation of line.

Q: Find the curve whose slope at any point (x,y) is 6x^2−2x−5 if the curve is required to pass through…

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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