It depends on where points h and k are, in which parabola. Since you have chosen not to share that information, there cannot be any sensible answer to this question.
Y=3x^2 and this is in standard form. The vertex form of a prabola is y= a(x-h)2+k The vertex is at (0,0) so we have y=a(x)^2 it goes throug (2,12) so 12=a(2^2)=4a and a=3. Now the parabola is y=3x^2. Check this: It has vertex at (0,0) and the point (2,12) is on the parabola since 12=3x2^2
All of the points on a parabola define a parabola. However, the vertex is the point in which the y value is only used for one point on the parabola.
The extreme point it the highest or lowest point of the parabola (depending if it is concave downwards or upwards). It is the point of the parabola tat is closest to the focus. the extreme point lies on the axis of symmetry.
No, it does not. You can tell if something is a function or not by using the vertical line test. If there is more than one point at any vertical line, it is not a function.
"From the geometric point of view, the given point is the focus of the parabola and the given line is its directrix. It can be shown that the line of symmetry of the parabola is the line perpendicular to the directrix through the focus. The vertex of the parabola is the point of the parabola that is closest to both the focus and directrix."-http://www.personal.kent.edu/~rmuhamma/Algorithms/MyAlgorithms/parabola.htm"A line perpendicular to the axis of symmetry used in the definition of a parabola. A parabola is defined as follows: For a given point, called the focus, and a given line not through the focus, called the directrix, a parabola is the locus, or set of points, such that the distance to the focus equals the distance to the directrix."-http://www.mathwords.com/d/directrix_parabola.htm
We can draw 3 normals to a parabola from a given point as the equation of normal in parametric form is a cubic equation.
This is called the 'standard form' for the equation of a parabola:y =a (x-h)2+vDepending on whether the constant a is positive or negative, the parabola will open up or down.
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At any point on the y-axis, the x-coordinate is zero. In the equation of the parabola, set x=0. Tidy it up, and you have " Y = the y-intercept ".
No you can't. There is no unique solution for 'x' and 'y'. The equation describes a parabola, and every point on the parabola satisfies the equation.
It is the parabola such that the coordinates of each point on it satisfies the given equation.
Y=3x^2 and this is in standard form. The vertex form of a prabola is y= a(x-h)2+k The vertex is at (0,0) so we have y=a(x)^2 it goes throug (2,12) so 12=a(2^2)=4a and a=3. Now the parabola is y=3x^2. Check this: It has vertex at (0,0) and the point (2,12) is on the parabola since 12=3x2^2
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There are several ways of defining a parabola. Here are some:Given a straight line and a point not on that line, a parabola is the locus of all points that are equidistant from that point (the focus) and the line (directrix).A parabola is the intersection of the surface of a right circular cone and a plane parallel to a generating line of that surface.A parabola is the graph of a quadratic equation.
The coordinates will be at the point of the turn the parabola which is its vertex.
A parabola is NOT a point, it is the whole curve.