Prove that if a parabola crosses the x-axis twice, the x-coordinate of the vertex of the parabola is halfway between the x-intercepts.

Q: when is the vertex of a parabola the minimun point? When is it the maximum point

A: Given query is to find that when is the vertex of a parabola the minimun point? When is it the…

Q: Find the x-intercepts and the coordinates of the vertex for the parabola y = x^2 – 2x + 1. If there…

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Q: Sketch the parabola f (x) = 2x2 - 4x.

A: Given: f(x) = 2x2-4x To sketch: The given parabola.

Q: 7. Determine all values of a that will cause the parabola y=ax² +10x+1 to cross the x-axis at two…

A: 7) y=ax2+10x+1 ...................eq (1) For parabola to cross the x- axis put y=0 0=ax2+10x+1…

Q: 3. A quadratic function will produce a parabola as a graph because A quadratic function will produce…

A: A quadratic function will produce a parabola as a graph

Q: Find the equation of the parabola whose axis is parallel to the x-axis and passes through the points…

A: We will find out the required value.

Q: Find the standard equation of any parabola that has vertex V.

A: The equation is a statement that consists of equal symbol between two algebraic expressions. The…

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

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Q: 3. Write an equation for the parabola with vertex at (2, 3), opening upward, and with no vertical…

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Q: A parabola with vertex (2, –3)and y-intercept (0, 5) can be expressed in vertex form as f(x) = (x –…

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

A: Given:Vertex=0,0Directrix y=-3Equation of parabola:x-h2=4py-k

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 with axis parallel to the x-axis, whose vertex is at (-1,7) and…

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Q: Suppose you are given the x-coordinate of a point on a parabola. How can you find the matching…

A: According to Bartleby guidelines, only one question can be solved at a time. Kindly post other…

Q: 5. If graphed, which of the following parabolas would lie entirely below the x-axis? (1) y=x² +5x+10…

A: We’ll answer the first question  . Please submit a new question specifying the one you’d like…

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

A: Given:To Find the standard equation of a parabola that has a vertical axis and lineformula of…

Q: Find an equation for the parabola that has its vertex at (1, 2) and its focus at (4, 2).

A: The vertex of the parabola is the point of intersection parabola with its axis. The general form of…

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

A: As per our guidelines we are supposed to answer only one question at a time. So submit the other…

Q: Graph the parabola: f(x)=0.5x^2-2. Show all work.

A: We have given a function,

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

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Q: The point (1,2) lies on the parabola: y 3x2 -2x+2 %3D

A: Thanks for the question :)And your upvote will be really appreciable ;) False statement (1,2) does…

Q: Find the x intercepts and the coordinates of the vertex for the parabola y = x^2 + 4x -21. If there…

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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: 2. What is the vertex of the parabola y = (x + 6) - 9?

A: the general equation of the parabola = (x-a)^2 = 4 c (y-b)  where a and b are the vertices of the…

Q: Find an equation of the parabola that satisfies the given conditions.Vertex at the origin, symmetric…

A: Since the parabola is symmetric to the y-axis and has vertex at the origin, The equation of the…

Q: The vertical line passing through the vertex of a parabola iscalled the_________

A: Solution:GivenThe vertical line passing through the vertex of a parabola is called the ...........

Q: The parabola y =- x² + x +1 opens

A: Let y = ax2+bx+cIf a>0 then parabola open upwardIf a< 0 then parabola opens downward.

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

A: We have Vertex=(0,0)Directrix x=-15

Q: The area bounded by the parabola y2 = 4ax, its axis, and its latus rectum revolves  about the x-

A: The given equation of parabola is y2=4ax. The objective is to calculate the area bounded by the…

Q: Find the standard equation of any parabola that has vertex V.

A: V-2,0

Q: A parabola has its turning point at x = -4 and one of the x-intercepts is x = -3. What is the x…

A: Given Data: The x coordinates of the turning point of the parabola is: x=-4 One of the x-intercepts…

Q: Is and directrix of the parabola: (y-7)²-6(x+9)

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

A: Given query is to find the equation of the paraola.

Q: the length of the latus rectum of the parabola 4y=x^2-6x+21 is

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Q: Suppose that a point A(6,4) lies on a parabola whose focus is at (-1, 3). What is the length of its…

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Q: Find an equation for the set of  all possible vertex points of a parabola that has an x-intercept at…

A: Consider that the origin (0, 0) is shifted to a point (h, k). Thus, any point (x, y) will be shifted…

Q: 5. A parabola has its turning point at x = -4 and one of the x-intercepts is x= -3. Ба What is the x…

A: From the given data: Parabola has a turning point at x=-4 That is x-coordinate of the vertex is…

Q: Obtain the X-value of vertex for the parabola defined by y = x2 +8x - 5

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Q: Find the standard equation of any parabola that has vertex V.

A: Standard equation of a parabola with vertical axis. The graph of the equation y=ax-h2+k for a≠0 is a…

Q: If a is greater than or equal to zero the equation of the parabola is of the form?

A: Parabola is a three dimensional curve, where any point is at fix distance from the point called…

Q: Consider the parabola given by the equation: f(x) = - 4x – 12x - 7 |

A: Given: fx=-4x2-12x-7

Q: 8. Use the discriminant to determine the number of x-intercepts of the parabola g(x) = 4x² + 3x – 3.…

A: Concept:[a] If the discriminant is positive, the parabola has two x-intercept.[b] if the discriminat…

Q: Find the equation for the parabola that has its vertex at the origin and has directrix at…

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Q: The vertex of the parabola f(x) = a+ 14z + 10 is %3D о (-14, -63) о (-21, -39) о (-14, -39) о (-7,…

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Q: Find an equation for the parabola that has its vertex at the origin and has a directric at x=1/29

A: We want to find out the equation of the parabola.

Q: Find the vertex and length of the latus rectum for the parabola. y = (x - 2)2 - 9 Vertex: (x, y) = (…

A: Topic = Parabola

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

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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.