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Probably the easiest way to do that is with a bit of calculus. You can take it's derivative, which gives you the slope of the tangent to that parabola. The point at which that slope is equal to zero is where the vertex lies. For instance:
f(x) = 6x2 + 7
f'(x) = 12x
f'(x) = 0 when x = 0, so the vertex is as point (0, 7)
g(x) = 2(x - 3)2 + 1
g(x) = 2x2 - 12x + 10
g'(x) = 4x - 12
g'(x) = 0 when x = 3, so the vertex is at point (3, 1)
More generically:
f(x) = a(x - b)2 + c
f(x) = ax2 - 2abx + b2 + c
f'(x) = 2ax - 2ab
f'(x) = 0 when x = b, so the vertex is at point (b, c)
which conveniently demonstrates another technique of finding the vertex of the parabola. If you convert it to the format f(x) = a(x - b)2 + c, your vertex will always be at point (b, c).
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How do you graph parabola given its vertex?
The vertex of a parabola doe not provide enough information to graph anything - other than the vertex!
What is the relationship of a vertex to a parabola?
The vertex is either the minimum (very bottom) or maximum (very top) of a parabola.
To find the value of a in a parabola opening up or down, subtract the y-value of the parabola at the vertex from the y-value of the point on the parabola that is one unit to the of the vertex?
right
To find the value of a in a parabola opening left or right subtract the x value of the parabola at the vertex from the x value of the point on the parabola that is one unit the vertex?
Above
An equilateral triangle is inscribed in a parabola with its vertex at the vertex of the parabola how do you find the length of the equilateral triangle?
First you need more details about the parabola. Then - if the parabola opens upward - you can assume that the lowest point of the triangle is at the vertex; write an equation for each of the lines in the equilateral triangle. These lines will slope upwards (or downwards) at an angle of 60°; you must convert that to a slope (using the tangent function). Once you have the equation of the lines and the parabola, solve them simultaneously to check at what points they cross. Finally you can use the Pythagorean Theorem to calculate the length.
The vertex of this parabola is at (-2, -3) When the x-value is -1, the?
Y=a(x-h)+k is the vertex formula. Since the vertex is at (-2,-3) this parabola has the equation: y=a(x+2)^2-3 We can plug in x=-1 but we really need to know a, to solve for y. ( we can solve it, but we will have an a in the solution)
What the the vertex of a parabola?
The vertex would be the point where both sides of the parabola meet.
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)
How do you do a parabola?
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.
To find the value of a in a parabola opening up or down subtract the y-value of the parabola at the vertex from the y-value of the point on the parabola that is one unit to the of the vertex?
To find the value of a in a parabola opening up or down subtract the y-value of the parabola at the vertex from the y-value of the point on the parabola that is one unit to the right of the vertex.
How do you graph parabola given its vertex?
The vertex of a parabola doe not provide enough information to graph anything - other than the vertex!
What is the relationship of a vertex to a parabola?
The vertex is either the minimum (very bottom) or maximum (very top) of a parabola.
What is the vertex of a parabola?
the vertex of a parabola is the 2 x-intercepts times-ed and then divided by two (if there is only 1 x-intercept then that is the vertex)
The is the extreme point of a parabola and is located halfway between the focus and directrix?
The vertex -- the closest point on the parabola to the directrix.
Is knowing the coordinates of the vertex of a parabola enough to determine the domain and range?
i think that the range and the domain of a parabola is the coordinates of the vertex
A parabola that opens upward?
Is a parabola whose directrix is below its vertex.
What do you call the maximum or the minimum of a parabola?
A parabola's maximum or minimum is its vertex.
