Given the parent function: y= x², write the equation to translate the parabola vertically up 4 units and compressed by a factor of 3

Q: Find the standard equation of the parabola with directrix x + 1 = 0, axis y = 1 and the length of…

A: If the axis of parabola is y = 1, then the parabola is horizontal. As we know that the standard…

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: What is the nearest distance from the point P(6,0) to the parabola? y^2=8x

A: GivenP(6.0)y2=8x To find nearest distance

Q: Find the x-intercepts of the parabola given by the equation. (If an answer does not exist, enter…

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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: Graph the given parabola and find its focus: Y=X squared

A: The given equation of parabola is: y=xory2=x  where x > 0

Q: Complete the square for x and for y An elliptical room is designed to function as a whispering…

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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: Classify the following equations as elliptic, parabolic or hyperbolic: а) и, — 4uxx = 0. - b) и, —…

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Q: Consider the parabola y = -x +4x + 9 and the line y=2x + 1. Solve for the x-coordinates at their…

A: x - coordinates of the point of intersection = ?

Q: solve for the focus of the parabola 8y = -x2 + 4x + 36

A: Solution:-     As we know,           The equation of a parabola in a vertex form is…

Q: A parabolic arch has an equation of 7x + y- 260 0. Find the maximum height of the arch. units

A: The equation of parabolic arch is: 7x2+y-260=0

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

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Q: Find the equation of the parabola with directrix x + 1 = 0, axis y = 2, and latus rectum 3.

A: Given :          The equation of directrix of the parabola is x + 1 = 0          The length of the…

Q: If the axis of symmetry of a parabola is given by x = 4, is it possible for the directrix to have…

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Q: Graph the function ?(?)=?2+2?−10f(x)=x2+2x−10by using completing the square to rewrite in vertex…

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Q: On one set of coordinate axes, graph the family of parabolas f(x) = x2 + bx + 1 for b = - 4, b = 0,…

A: Consider the given general form of the equation. fx=x2+bx+1 Put b=-4 in the equation. fx=x2−4x+1 Put…

Q: Solve for y by taking the square root of both sides of the equation. f (z) = +9,z <9

A: The highlighted graph is here the actual graph of the given equation. Where as other blue colour…

Q: Given the parabola f(X) =-X²+10x +14, find the following for this parabola: A) The value of f(-1) =…

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Q: The height of a body moving vertically is given by s = - gt2/2 + y0 t + s0, g&gt;0, with s in meters…

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Q: Find a point on the parabola y - x* + 9 which is closest to the origin.

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Q: Find the x-intercepts of the parabola given by the equation. (If an answer does not exist, enter…

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Q: Find the coordinates of the point on the parabola y = x² which is closest to the point (3, 0).

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Q: find the points on the parabola y=x^2 closest to the point (0,1)

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Q: Find an equation for the parabola that has its vertex at the origin and satisfies the given…

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Q: b) Determine the concavity, Y-Intercept, X- intercept of the quadratic equation And sketch the…

A: Clearly shows the turning poin of the quadratic equation is (10, -50)

Q: The parabola y = x² is shifted up by 7 units and to the left by 1 unit. What is the equation of the…

A: Equation of parabola is given as y=x2. If the parabola is shifted by a units and to the left by b…

Q: Find the shorted distance from the point A(2, to a point on the parabola y = x². And find the point…

A: Let (x,y) = (x,x2) point on the parabola is closest to A Distance between (2 , 1/2) and (x,x2) is:…

Q: Assume that from 1860 to 1920, the city of Painesville’s population experienced uninhibited growth.…

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Q: For the parabola y=-4(x+1)^2 - 3, the range is...?

A: For  y=ax2+bx+c  with vertex      (x1  y1)

Q: Find an equation for the parabola shown in the figure.

A: We have given Vertex: 1, 0 Focus:6, 0   The given graph is symmetric about x-axis. Equation of the…

Q: 3. Complete the table for each parabola Equation Y= -0.4(x-2)2 Y = 3(x + 5) 2 + 3 Direction of…

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Q: If the vertex of the parabola f (x)= x² +bx+c is at (7, -4), find b and c. (Note: a = 1).

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Q: Find the point(s) on the parabola x =y closest to the point (0,3)

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Q: Find the x-intercepts of the parabola given by the equation. (If an answer does not exist, enter…

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Q: Find the standard equation of a parabola if its latus rectum measures 9 units, axis at y = 3, p is…

A: Let's find standard equation of a parabola.

Q: Find the equation of the parabola with directrix x + 1 = 0, axis y = 2, and latus rectum 2.

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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: Find an equation for the contour of f(x, y) = 2x2y + 6x + 10 that goes through the point (2, -2).

A: We have to find an equation that is the contour of  f(x,y)=2x2y+6x+10      that goes through the…

Q: Given the function h(c) = 2c+8, solve for h(c)3D2. Provide your answer below

A: Given function h(c)=2c+8c

Q: Find the point on the parabola y=x2 closest to (6,3

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Q: A parabola is modeled with the equation x2 – 6x + 4y – 19 = 0. Which is the domain and range of the…

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Q: Write the equation (f (x)) of the parabola satisfying the points a, (a + b) / 2 and b. where the…

A: Consider the given Simpson’s 13 rule: The objective is to find the equation fx of the parabola…

Q: The following equation represents the relationship between hours of TV watched per day (x) and the…

A: We have to predict value..

Q: Find the equation of the parabola with directrix y = 3, axis x = 0, and latus rectum 4

A: Given: Equation of directrix:y=3……1Equation of axis:x=0……2Length of latus rectum:4……3

Q: Given x2 = 4py with p&gt; 0, the parabola opens (upward/downward/left/right).

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Q: Find the x-intercepts of the parabola given by the equation. (If an answer does not exist, enter…

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Q: Solve the following problems. Show the complete solution. What is the equation of the line to the…

A: For tangent line first  find the slope of the line at that point ..then find the equation of line

Q: Consider the parabola given by the equation: y=x2+10x+9 Find the two values of x that correspond to…

A: Given information: The equation is y=x2+10x+9. Calculation: Find the x-intercepts of the equation…

Q: A population of bacteria is growing according to the equation P(t) = 1150e.18t, Estimate when the…

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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.