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What is a fixed point that lies on the axis of symmetry of a parabola but not on the parabola?
There would be an infinite number of such points. One way to find them is as follows:
Let's take a generic parabola:
y = ax2 + bx + c
Grab it's derivative with respect to x:
dy/dx = 2ax + b
Let that equal zero, and solve for x:
0 = 2ax + b
2ax = -b
x = -b/2a
Now we know the x-coordinate of all points that lie on it's line of symmetry. The only one that we don't want being the one that falls on the curve itself. We can find it's y-coordinate by plugging our x-coordinate into the original parabola
y = ax2 + bx + c
y = a(-b/2a)2 + b(-b/2a) + c
y = a(b2/4a2) - b2/2a + c
y = b2/4a - b2/2a + c
y = b2/4a - 2b2/4a + c
y = -b2/4a + c
So there we have it. Given a parabola in the format ax2 + bx + c, all points that lie on it's axis of symmetry have an x-coordinate of -b/2a, and a y-coordinate other than -b2/4a + c
What else can I help you with?
Which point of parabola is on the axis of symmetry?
Its extremum is on its axis of symmetry.
What is the point of which a parabola intersects the axis of symmetry called?
if it opens up then the point is called the minimum if it opens down its called the maximum
What is the axis of symmetry for the parabola with vertex (-2 -4) and directrix y 1?
The axis of symmetry is x = -2.
Why is the vertical line that passed through the vertex of a parabola called the axis of symmetry?
K
What is the focus of a parabola?
The focus of a parabola is a fixed point that lies on the axis of the parabola "p" units from the vertex. It can be found by the parabola equations in standard form: (x-h)^2=4p(y-k) or (y-k)^2=4p(x-h) depending on the shape of the parabola. The vertex is defined by (h,k). Solve for p and count that many units from the vertex in the direction away from the directrix. (your focus should be inside the curve of your parabola)
Which point of parabola is on the axis of symmetry?
Its extremum is on its axis of symmetry.
What is the extreme point on a parabola?
The highest or lowest point of the parabola, it is the point that is closest to the focus. The extreme point lies on the axis of symmetry
Where is the axis of symmetry of a parabola located?
Parallel to the y-axis, going through the highest/lowest point of the parabola (if the parabola is negative/positive, respectively).
What line divides the parabola where one point on one side of the parabola and the corresponding point on the other side?
the axis of symmetry
What is the point directly above the focus?
The point directly above the focus is the vertex of the parabola. The focus is a specific point on the axis of symmetry of the parabola, and the vertex is the point on the parabola that is closest to the focus.
What is the extreme point of a 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.
Parts of a parabola?
There's the vertex (turning point), axis of symmetry, the roots, the maximum or minimum, and of course the parabola which is the curve.
A parabola has an axis of symmetry.?
Yes, it does.
Where is the line of symmety located on a parabola?
The line of symmetry located on a parabola is right down the center. A parabola is a U shape. Depending on the direction of the parabola it either has a x axis of symmetry or y axis of symmetry. You should have two equal sides of the parabola.
An equation of a parabola that has x equals 2 as its axis of symmetry is?
How about y = (x - 2)2 = x2 - 4x + 4 ? That is the equation of a parabola whose axis of symmetry is the vertical line, x = 2. Its vertex is located at the point (2, 0).
What is the point of which a parabola intersects the axis of symmetry called?
if it opens up then the point is called the minimum if it opens down its called the maximum
What is the axis of symmetry for the parabola with vertex (-2 -4) and directrix y 1?
The axis of symmetry is x = -2.
