What is the equation of the quadratic function whose graph is a parabola which opens to the left, vertex at (0, 0), focus at (-2, 0), endpoints of the latus rectum are (-2, 4) and (-2, -4) with the equation of the directrix = 2?

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-…

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

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Q: What is the length of the latus rectum of a parabola having its vertex at the origin and focus at…

A: The length of latus rectum of parabola = 4a

Q: A parabola of y=x^2 has been regraphed and now sits with each side plotted at (-3,5) and (3,5) and…

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Q: Show the complete solutions. Family of horizontal parabolas whose h to k ratio is 2.

A: Let's find differential equation.

Q: "What is the families of the curve of all Parabolas with axis parallel to the x-axis

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Q: Suppose that point A(-2, -1) lies on a parabola with horizontal principal axis and whose vertex is…

A: Suppose that point A(-2, -1) lies on a parabola with horizontal principal axis and whose vertex is…

Q: Write a quadratic equation for the parabola that passes through the point (-2, 12) with roots (-5,…

A: Solution is given below:

Q: 15 2. Find the equation of a parabola through(-, 2) and (0,–1) whose axis is parallel 4 to the…

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Q: Write the equation of the parabola in vertex or intercept form. 11. 12. YA (1, 25) (4, 6) 10 -2-…

A: Let's find.

Q: Find the standard form of the equation of the parabola with the given characteristics. vertex: (2,4)…

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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: 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 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: How to write the equation of the parabola with a vertex of (0,0) and axis of symmetry the y- axis;…

A: We have to write the equation of parabola with vertex (0,0) and a point in the parabola that is…

Q: If a parabola has a minimum at the point (-2, 4), the parabola has... O one positive x-intercept,…

A: The vertex form of a parabola is defined by the equation, . If a parabola faces up, it has the…

Q: A rectangle has its base on the x-axis and its upper two vertices on the parabola y = 12 - x. What…

A: Given that the rectangle has its base on x- axis and its upper two vertices on parabola let us take…

Q: A point moves on the parabola y2 = 8 in such a way that the rate of change of the ordinate is always…

A: The given parabolic curve is, y2 = 8x    ...(1)   It is given that the rate of change of ordinate is…

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: Find the equation of a parabola whose vertex is located at (2, −3) and whose focus is located at…

A: Given: vertex: 2,-3focus: 0,-3 To Find: Equation of a parabola. Concept: Horizontal…

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: In Exercises 17–27, use the vertex and intercepts to sketch the graph of each quadratic function.…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

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: What is the equation of parabola in standard form whose focus is at (-4,0) and the directrix is at…

A: Note that, the equation of the parabola with the directrix x+a=0 and the focus (a,0) is y2=4ax.

Q: Find the equation of a parabola whose latus rectum is joined by points (2, 1) and (-4, 1)

A: Use equation of parabola

Q: 5) Find the equation for the parabola that has its vertex at (5,-3), axis parallel to the y-axis,…

A: given,         vertex of parabola =5,-3  and passing through the point 9,5

Q: The parabola passes through the points (−3/2, – 1), (1, 5) and vertex is at (0, 4) with a horizontal…

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Q: Find the equation of the line normal to the parabola y = x2 - 6x + 12 perpendicular to the line that…

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Q: Find the points of intersection between the parabolas y = 6 - x 2 and y = x 2 - 2. %3D

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Q: 7. Find the equation of the parabola in standard form vertex at the origin passing through the point…

A: The equation of the parabola in vertex form with vertex (h.k) is y = a(x-h)2+k Here the vertex is at…

Q: Graphically, parabolas can be viewed as the set of all points whose distance from _____ is equal to…

A: Graphically, parabolas can be viewed as the set of all points whose distance from _____ is equal to…

Q: Find the equation of a parabola that has a vertex of (7, -4) and contains the point (0, 94),…

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Q: b. Family of parabolas whose vertex is along the line y -2, %3D

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Q: How do you find the standard form of the equation of the parabola with the given characteristic(s)…

A: Given vertex is at origin i.e (h,k) = (0,0) To find the standard equation of parabola

Q: What point on the parabola y = 3- x² is closest to the point (3,3)? The point on the parabola y = 3…

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Q: 7. Write an equation for each parabola a) 0, 11) 8- 4- (4, –5) b) | YA |(-6, 4) 4- (-5.3) 2 -6 -2 0…

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Q: Find the equation of a parabola that has a vertex of (2, -4) and contains the point (1, -7).…

A: Given  Vertex of parabola (2,-4)  And contains the points (1,-7)

Q: What point on the parabola y = 1-x is closest to the point (1,1)? The point on the parabola y = 1-x2…

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Q: What is the correct quadratic function for this parabola?

A: Note: General equation of parabola is y-k = 4a(x-h)^2 and x-h = 4a(y-k)^2  Vertex for both the form…

Q: A parabola goes through  points (1,0), (2,3), (-1,0). Find the equation of this function.

A: Consider the given points (1,0),(2,3) and (-1,0)Let the equation of parabola is

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: Write the equation of two different parabolas that have a vertex of (3,-1), and that pass through…

A: Vertex is ( 3 , -1 )  and point (0, 2 ) So Now equation of parabola is given by    y = a ( x - h )2…

Q: I graphed a hyperbola centered at the origin that had y-intercepts but no x-ntercepts.Determine…

A: Types of hyperbolas: 1. Vertical hyperbola: Its graph contains two vertical parabolas which are…

Q: Determine an equation of the parabola with the vertex at (-2, 5) and passes through the point (-3,…

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Q: Find the Equation of a Quadratic (Parabola) Given 3 Points y=a^2+bx+c (0,0), (-3,3), (3,3) Also,…

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Q: 3. Express the quadratic in vertex form. Make sure to clearly show every step in completing the…

A: Given equation is y=2x2-12x+16 express it in vertex form

Q: Suppose the axis of a parabola is parallel to the yy-axis and passing through the points (0,3),…

A: Given that, the axis of a parabola is parallel to the y-axis. Let the Vertex of the parabola (h, k)…

Q: A suspension bridge has two supporting towers with a cable secured at either end of the span and…

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.