A parabola
It is a square root mapping. This is not a function since it is a one-to-many mapping.
A parabola is a graph of a 2nd degree polynomial function. Two graph a parabola, you must factor the polynomial equation and solve for the roots and the vertex. If factoring doesn't work, use the quadratic equation.
A parabola is NOT a point, it is the whole curve.
The derivative if a function is basically it's slope, or its rate of change. An example is the function y = 4x - 6. This is a line with a slope of 4. The derivative is y' = 4. Another example is the function y = 3x2. This is a parabola with a vertex at (0,0). Its derivative is y' = 6x. At x = 0, the slope of the parabola is 6*0, which is 0, since this is the vertex of the parabola. To the left, at x is -4 for example, the derivative (and therefore slope) is negative. To the right, at x = 5 for example, the derivative is positive. The farther away from the vertex, the greater the value of the derivative so the the slope of the function increases as you move away from the vertex (it gets steeper).
No. It can also be a circle, ellipse or hyperbola.
An x2 parabola will always have one vertex, but depending on the discriminant of the function (b2-4ac) the parabola will either have 2 roots (it crosses the x-axis twice), 1 repeating root (the parabola meets the x-axis at a single point), or no real roots (the parabola doesn't meet the x-axis at all)
The graph of a quadratic function is always a parabola. If you put the equation (or function) into vertex form, you can read off the coordinates of the vertex, and you know the shape and orientation (up/down) of the parabola.
A parabola has no endpoints: it extends to infinity.A parabola has no endpoints: it extends to infinity.A parabola has no endpoints: it extends to infinity.A parabola has no endpoints: it extends to infinity.
It is the bisector of any 2 parallel chords drawn to the parabola. It is always parallel to the axis of the parabola.
A 'Parabola'
Y = X2 ===== The graph of this parabola is crossed only at a point and once by a vertical line, so it is a function. Passes the vertical line test.
No, but any parabola can be transformed into the form y = x^2.
A parabola
The parabola
It is a function because for every point on the horizontal axis, the parabola identified one and only one point in the vertical direction.
It is a square root mapping. This is not a function since it is a one-to-many mapping.