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What is the equation of the function of the parabola that contains the points 0 0 20 12 0 40?
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:
- (0, 0) → 0 = 0²x + 0b + c → 0 = c
- (20, 12) → 20 = 12²a + 12b + c → 20 = 144a + 12b + c
- (0, 40) → 0 = 40²a + 40b + c → 0 = 1600a + 40b + c
From equation 1, c = 0, so substituting in the second and third equations gives two new equations involving two unknowns:
- 20 = 144a + 12b
- 0 = 1600a + 40b
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
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What are the zeros of a parabola?
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.
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.
Is a parabola a line?
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.
What is the answer to y equals x2?
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)
How many vertices points and edges does a parabola have?
A parabola has one vertex (but not in the sense of an angle), infinitely many points and no edges.
