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How does an equation for a sideways parabola look like?
An equation for a sideways parabola can be expressed in the form ( y^2 = 4px ) for a parabola that opens to the right, or ( y^2 = -4px ) for one that opens to the left. Here, ( p ) represents the distance from the vertex to the focus. The vertex of the parabola is at the origin (0,0), and the axis of symmetry is horizontal. If the vertex is not at the origin, the equation can be adjusted to ( (y-k)^2 = 4p(x-h) ), where ((h, k)) is the vertex.
How do you graph y equals x2?
The graph is a parabola facing (opening) upwards with the vertex at the origin.
How do you graph yx2?
To graph the equation ( y = x^2 ), first recognize that it represents a parabola opening upwards. Plot key points, such as ( (0, 0) ), ( (1, 1) ), ( (-1, 1) ), ( (2, 4) ), and ( (-2, 4) ). Connect these points smoothly, ensuring the curve is symmetric about the y-axis. The vertex of the parabola is at the origin, and the graph will extend infinitely upwards as ( x ) moves away from zero.
How do we know when an equation represents a proportional relationship?
If it passes through the origin
What is the standard equation for vertex at origin opens down 1 and 76 units between the vertex and focus?
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.
How does an equation for a sideways parabola look like?
An equation for a sideways parabola can be expressed in the form ( y^2 = 4px ) for a parabola that opens to the right, or ( y^2 = -4px ) for one that opens to the left. Here, ( p ) represents the distance from the vertex to the focus. The vertex of the parabola is at the origin (0,0), and the axis of symmetry is horizontal. If the vertex is not at the origin, the equation can be adjusted to ( (y-k)^2 = 4p(x-h) ), where ((h, k)) is the vertex.
What is the equation of a parabola with a vertex at 0 0 and a focus at 0 6?
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
How do you graph y equals x2?
The graph is a parabola facing (opening) upwards with the vertex at the origin.
What is the standard equation of a parabola that opens up or down and whose vertex is at the origin?
focus , directrix
How do you graph yx2?
To graph the equation ( y = x^2 ), first recognize that it represents a parabola opening upwards. Plot key points, such as ( (0, 0) ), ( (1, 1) ), ( (-1, 1) ), ( (2, 4) ), and ( (-2, 4) ). Connect these points smoothly, ensuring the curve is symmetric about the y-axis. The vertex of the parabola is at the origin, and the graph will extend infinitely upwards as ( x ) moves away from zero.
How do we know when an equation represents a proportional relationship?
If it passes through the origin
What is the standard equation for vertex at origin opens down 1 and 76 units between the vertex and focus?
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.
What does 4 stands for in equation of parabola square of square of y equals 4ax?
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)
How do you get a parabola with only one x intercept?
To have a parabola with only one x-intercept, the vertex of the parabola must lie on the x-axis. This means the parabola opens either upwards or downwards, depending on the coefficient of the squared term in the equation. If the coefficient is positive, the parabola opens upwards, and if it is negative, the parabola opens downwards. By adjusting the coefficients in the equation of the parabola, you can position the vertex such that there is only one x-intercept.
What equation correctly represents a circle centered at the origin with a radius of 10?
x^2 + y^2 = 100
What is the range of the function on the graph?
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.
What is the focus of the parabola y 4x2?
The equation of the parabola ( y = 4x^2 ) can be rewritten in the standard form ( y = 4p(x - h)^2 + k ), where ( (h, k) ) is the vertex. Here, it is clear that the vertex is at the origin (0, 0) and ( 4p = 4 ), giving ( p = 1 ). The focus of the parabola is located at ( (h, k + p) ), so the focus is at the point ( (0, 1) ).
