As there is a repeated x-coordinate, x = f(y), giving:
As it is a parabola, x = ay² + by + c, so substituting the known points:
From equation 1, c = 0, so substituting in the second and third equations gives two new equations involving two unknowns:
0 = 40a + b
→ b = -40a
This can be substituted back into the first to give:
20 = 144a + 12 b
→ 20 = 144a + 12(-40a)
→ 20 = 144a - 480a
→ 20 = -336a
→ a = -5/84
→ b = -40a = -40(-5/84) = 50/21
→ x = -5/84 y² + 50/21 y
→ 84x = -5y² + 200y
→ 84x = 200y - 5y²
The parabola has equation 84x = 200y - 5y²
A parabola which goes through (0, 0) and (0, 40) cannot be a function: no function can be one-to-many.
They are the x-values (if any) of the points at which the y-value of the equation representing a parabola is 0. These are the points at which the parabola crosses the x-axis.
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.
By the geometric definition of a line, it is represented by two points, and all points on the line are collinear, between or extrapolating to infinity from the straight line made by the two points. In other words, a line is straight, and can be represented by a binomial function (example: y=2x+1). A parabola is a function, but cannot be described mathematically as a line.
I'm guessing you mean y = x², which is the equation of a parabola. There is no one answer. Every point which lies on the parabola is the solution set to the equation. Some examples of points which satisfy this are: (0,0) (1,1) (2,4) (-3,9) (-5,25) and (½,¼)
A parabola has one vertex (but not in the sense of an angle), infinitely many points and no edges.
They are the x-values (if any) of the points at which the y-value of the equation representing a parabola is 0. These are the points at which the parabola crosses the x-axis.
-- The roots of a quadratic equation are the values of 'x' that make y=0 . -- When you graph a quadratic equation, the graph is a parabola. -- The points on the parabola where y=0 are the points where it crosses the x-axis. -- If it doesn't cross the x-axis, then the roots are complex or pure imaginary, and you can't see them on a graph.
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.
As it is a function and a parabola, it has many y-values. To find a certain one, you would plug a number in for x and solve it, or you could graph the equation see what points fall on the curve. In essence, that equation is the y-values.
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.
If you mean points of: (10, -2) and (20, -12) then it is a straigh line equation in the form of y = -x+8
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.
By the geometric definition of a line, it is represented by two points, and all points on the line are collinear, between or extrapolating to infinity from the straight line made by the two points. In other words, a line is straight, and can be represented by a binomial function (example: y=2x+1). A parabola is a function, but cannot be described mathematically as a line.
I'm guessing you mean y = x², which is the equation of a parabola. There is no one answer. Every point which lies on the parabola is the solution set to the equation. Some examples of points which satisfy this are: (0,0) (1,1) (2,4) (-3,9) (-5,25) and (½,¼)
Choose the equation of the line that contains the points (1, -1) and (2, -2).
A parabola has one vertex (but not in the sense of an angle), infinitely many points and no edges.
If a quadratic function has the points (-4,0) and (14,0), what is equation of the axis of symmetry?