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What is the equation of the function of the parabola that contains the points 0 0 20 12 0 40?
Wiki User
∙ 7y ago
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
Wiki User
∙ 7y ago
Wiki User
∙ 7y agoA parabola which goes through (0, 0) and (0, 40) cannot be a function: no function can be one-to-many.
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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.
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What is the answer to y equals x2?
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