The parabola y = -r² + 4 has vertex labelled P and intersects the r-axis at the points labelled A and B. The parabola is translated from its original position so that its vertex moves along the line y = x +4 to the point Q. In this new position, the parabola intersects the r-axis at the points labelled B and C. Determine the coordinates of C.

Q: The parabola y = ² is changed to the form y = a (x − p)² + g by translating the parabola 2 units…

A: The parabola y=x2 is changed to the form y=ax-p2+q by translating the parabola 2 units down and 3…

Q: Suppose a and b are positive numbers. Sketch the parabolas y2 = 4a2 - 4ax      and         y2 = 4b2…

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Q: For the parabola y2 = 4ax, the line segment joining the two points (a, 2a) and (a, - 2a) is called…

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Q: 9. Sketch the parabola y =-x +8x-12, show all the intercepts, the axis symmetry and the vertex

A:

Q: 2. Give the equation in the form ax + by +c = 0 fo the line & passing through C(-4, 6) with slope 1…

A: From the given data we have to find the following value.

Q: Q4) Find the y-intercept, x-intercept(s) and the vertex point for the parabola y = x2 + 6x + 5 then…

A: Given: Parabola: y=x2+6x+5 To Find:  The y-intercept, x-intercepts and the vertex point for the…

Q: graph the parabola y=(x-5)2-2

A: Consider the given equation

Q: Graph the parabola. y? = 4x 12 10- 6+ 4+ ? -12 -10 -6 -4 -2 10 12 -2- -6. -8- -10 -12+ og

A: Given curve is a parabola  We have draw the graph of parabola.  Given parabola is a type of opening…

Q: Write an equation for the parabola with axis horizonal, vertex on the y-axis, and containing the…

A:

Q: What is the equation of the parabola containing the points (0, 5), (–1,9), and (2, 3)? O y = r-z+5 O…

A: The standard form of a parabola is y=ax2+bx+c. The required parabola passes through the 3 points are…

Q: Suppose a parabola has vertex (-8, -7) and also passes through the point (-7, -4). Write the…

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Q: Find all hyperbolic lines that passes through i +1 and parallel to the y-axis.

A: Find all hyperbolic lines that passes through i+1 and parallelto the y-axis.

Q: Write an equation for the parabola whose vertex is at (3, 6 ) and which passes through point (4, 4…

A: Given Data: The vertex of the parabola is: (h, k)=(3, 6) The coordinate of a point on the parabola…

Q: Find the equation of the parabola with vertex at (2,-1), axis is parallel to the y-axis and passing…

A: Equation of parabola parallel to y axis is given by as: (x-h)²= 4a(y-k)

Q: Show, by completing the square, that the parabolay = ax2 + bx +c can be obtained from y = ax 2 by a…

A: The given equation of parabola is y=ax2+bx+c. Rewrite the above equation as follows.…

Q: Draw the graphs of the equations x-y+1=0 and 3x+2y-12=0. Determine the co-ordinates of vertices of…

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Q: 2. a. f(x) = 5x² + 40x + 77 b. y = 2r + 12x + 17 c. y = 2x – 8x + 1 d. y = 2x – 6x – 1 — 1

A: To write the vertex form of the given quadratic equations. Note that the vertex form of the…

Q: A parabola has a vertex at (4,-11) and runs through the point (8,-123). Determine the equation for…

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Q: Find an equation of the parabola with vertex (- 3, 4) and focus (1, 4)

A:

Q: 6) Write an equation of the parabola with the vertex (3, -1) and the focus (3, -5).

A: Equation of parabola is

Q: Arrange the parabolas represented by the equations according to the positions of their foci on the…

A: The standard form of a parabola is  (x – h)2 = a(y – k) where (h, k) is the vertex.

Q: Obtain the graph of the parabola y = -x? + 4x using transformations of the graph of y = x². Explain…

A: Given,  y=x2To Obtain: y=-x2+4x using transformation

Q: 6. Write the equation y = x² - 4x + 2 in vertex form.

A: Given, y=x2-4x+2

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.