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The standard equation for a Parabola with is vertex at the origin (0,0) is, x2 = 4cy if the parabola opens vertically upwards/downwards, or y2 = 4cx when the parabola opens sideways.

As the focus is at (0,6) then the focus is vertically above the vertex and we have an upward opening parabola.

Note that c is the distance from the vertex to the focus and in this case has a value of 6 (a positive number).

The equation is thus, x2 = 4*6y = 24y

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What is the coefficient of the squared term in the parabola's equation when the vertex is at 2 -1 and the point 5 0 is on it?

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Vertex = (3, - 2)Put in vertex form.(X - 3)2 + 2X2 - 6X + 9 + 2 = 0X2 - 6X + 11 = 0=============The coefficeint of the squared term is 1. My TI-84 confirms the (4, 3) intercept of the parabola and the 11 Y intercept shown by the function.


What is the line of symmetry for the parabola whose equation is y -x2 x 3?

Did you mean a parabola with equation y=3x^2? The line of symmetry is x=0 or the y-axis.


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Related Questions

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A parabola with an equation, y2 = 4ax has its vertex at the origin and opens to the right. It's not just the '4' that is important, it's '4a' that matters. This type of parabola has a directrix at x = -a, and a focus at (a, 0). By writing the equation as it is, the position of the directrix and focus are readily identifiable. For example, y2 = 2.4x doesn't say a great deal. Re-writing the equation of the parabola as y2 = 4*(0.6)x tells us immediately that the directrix is at x = -0.6 and the focus is at (0.6, 0)


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What is the coefficient of the squared term in the parabola's equation when the vertex is at 2 -1 and the point 5 0 is on it?

A parabola with vertex (h, k) has equation of the form: y = a(x - h)² + k → vertex (k, h) = (2, -1), and a point on it is (5, 0) → 0 = a(5 - 2)² + -1 → 0 = a(3)² -1 → 1 = 9a → a = 1/9 → The coefficient of the x² term is 1/9


The vertex of this parabola is at (-3 -1). When the y-value is 0 the x-value is 4. What is the coefficient of the squared term in the parabola's equation?

To find the coefficient of the squared term in the parabola's equation, we can use the vertex form of a parabola, which is (y = a(x - h)^2 + k), where ((h, k)) is the vertex. Here, the vertex is ((-3, -1)), so the equation becomes (y = a(x + 3)^2 - 1). Given that when (y = 0), (x = 4), we can substitute these values into the equation to find (a): [0 = a(4 + 3)^2 - 1 \implies 0 = a(7^2) - 1 \implies 1 = 49a \implies a = \frac{1}{49}.] Thus, the coefficient of the squared term is (\frac{1}{49}).