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The graph is a parabola facing (opening) upwards with the vertex at the origin.
Since the vertex is at the origin and the parabola opens downward, the equation of the parabola is x2 = 4py, where p < 0, and the axis of symmetry is the y-axis. So the focus is at y-axis at (0, p) and the directrix equation is y = -p. Now, what do you mean with 1 and 76 units? 1.76 units? If the distance of the vertex and the focus is 1.76 units, then p = -1.76, thus 4p = -7.04, then the equation of the parabola is x2 = -7.04y.
If it passes through the origin
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)
x2/a2 + y2/b2 = 1, is the equation of an ellipse with semi-major axes a and b (that's the equivalent of the radius, along the two different axes), centered in the origin.
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
The graph is a parabola facing (opening) upwards with the vertex at the origin.
focus , directrix
If it passes through the origin
Since the vertex is at the origin and the parabola opens downward, the equation of the parabola is x2 = 4py, where p < 0, and the axis of symmetry is the y-axis. So the focus is at y-axis at (0, p) and the directrix equation is y = -p. Now, what do you mean with 1 and 76 units? 1.76 units? If the distance of the vertex and the focus is 1.76 units, then p = -1.76, thus 4p = -7.04, then the equation of the parabola is x2 = -7.04y.
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)
x^2 + y^2 = 100
The range of a function is the set of Y values where the equation is true. Example, a line passing through the origin with a slope of 1 that continues towards infinity in both the positive and negative direction will have a range of all real numbers, whereas a parabola opening up with it's vertex on the origin will have a range of All Real Numbers such that Y is greater than or equal to zero.
When the vertex lies on the x-axis. For example x = y2, the vertex is at the origin, and the parabola is lying on its side.
x2/a2 + y2/b2 = 1, is the equation of an ellipse with semi-major axes a and b (that's the equivalent of the radius, along the two different axes), centered in the origin.
The displacement-time graph of a body moving with constant acceleration is a curve that is a quadratic function. It is a parabolic curve, where the slope represents the velocity of the body and the curvature represents the acceleration.
It is (x - a)^2 + y^2 = a^2 or, equivalently, x^2 + y^2 = 2ax.