What is the general equation of a parabola that opens upward with V(-1,2)?

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

A: Basic differentiation is required.

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-…

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Q: Write the equation of the hyperbola centered at the origin, with length of the horizontal transverse…

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Q: In which direction does the parabola x = -y 2 + 3 open?

A: x=-y2+3 There are two patterns for a parabola, as it can be either vertical (opens up or down) or…

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: The equation of a family of parabolas with axis parallel to the y-axis is

A: We will find the equation of family of parabolas with axis parallel to the y-axis .Below find the…

Q: Find the equation of the parabola with vertex (−3,1) and y-intercept 2(or (0,2)).

A: We have to find the equation of the parabola with vertex (−3,1) and y-intercept (0,2).

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

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Q: The vertical line passing through the vertex of a parabola is called the ......... .

A: Given The vertical line passing through the vertex of a parabola is called the ......... .

Q: What is the equation of the parabola which has vertex (1,2) and y-intercept y = 1?

A: See the details solution in below

Q: 2. What is the value of y anytime a parabola intersects the x-axis?

A: It is known that the value of y on x-axis is always 0.

Q: What is the equation of the parabola with axis parallel to the x-axis, whose vertex is at (-1,7) and…

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Q: Find the equation of the parabola and put it in the form f(x)= ax^2 +bx+c  Given:  vertex: (7, -4)…

A: Explained below

Q: What is the equation of the parabola with axis parallel to the x-axis, whose vertex is at (-1,7) and…

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Q: What is the equation of a hyperbola with major axis parallel to the y – axis?

A: The standard form of the equation of a hyperbola with center (h, k) and transverse(major) axis…

Q: Find the standard equation of a parabola that has a vertical axis and satisfies the given…

A: Vertex of the parabola is h, k=0, 5 & it passes through the point 2, -3. Now the equation of the…

Q: What is the equation of the parabola that has a max of (2,3), and passes through point (, -1)?

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

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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: ises 17–30, find the equations of the parabola

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Q: Write the equation of a parabola with vertex (0,0) and directrix y =-3

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Q: Consider a parabola that intersects the x-axis at points (-1, 0) and (3, 0).

A: We need to find an equation of parabola that intersects the x-axis at (-1, 0) and (3, 0). Thus,…

Q: Suppose that point A(-4,0) lies on a parabola whose focus is at (5,3). What is the length of the…

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Q: Find an equation of the parabola with vertex (2, 2) and directrix x = 8. 00 0=0 X Ś ?

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Q: What point on the parabola y=(6−x)2 is closest to the point (6​,6​)?

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Q: What is the equation of the parabola in general form given its vertex at (-1,-5) and focus at…

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Q: Define the term parabola?

A: Given: The term parabola.

Q: What is the axis of symmetry of the parabola with equation (y - 1) = 4 (x – 1) ?

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Q: Find an equation of the parabola with vertex (-5,-4) and directrx y =-11,

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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: I llustiate and Sketch the equation of parabola ?f vertex

A: General equation of parabola is of form y2=4ax or x2=4ay

Q: Find the equation for the parabola that passes through the point (-2, -4), with vertex at (3,1) and…

A: Given

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: How can we Find the slope of the parabola?

A: Let the equation of a parabola be: y^2 = 4ax

Q: What is the equation of the parabola with vertex (1, –11) and that passes through (–4, 64)?

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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 DE of parabolas with vertex and focus on the x-axis.

A: We know that equation of parabola when vertex and focus on the x-axis is, y2=4ax-h  where a and h…

Q: · Write an equation for the parabola with vertex at (4, –1), opening upward, and with a vertical…

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Q: What are the vertex and the axis of symmetry of the parabola shown in the diagram below? y

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Q: What is the equation of the standard parabola with its vertex at the origin that opens downward?

A: we have to find the equation of the standard parabola with its vertex at the origin that opens…

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: Find the equation of a parabola that has focus at (-4,0) and directrix 2

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Q: What is the Axis of Symmetry of the parabola represented by y = - = -x² – 3x + 7? O x = 3 O x = -3 O…

A: The axis of symmetry of a parabola is a vertical line that divides the parabola into two congruent…

Q: Describe how the parabolas y = x2 + bx change as b changes from -oo to oo.

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Q: Find the standard form of the equation of the parabola that has a vertex at (1,-3) and passes…

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Q: Find the equation in standard form of a parabola whose focus is at (-3,-2) and whose directrix is x:…

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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.