There are infinitely many equations; 4 possibilities are:
y = x² - 21
y = 29 - x²
x = y² - 21
x = 11 - y²
Given the focus as well would give an exact equation.
-1
Assuming the vertex is 0,0 and the directrix is y=4 x^2=0
y = -5 By using calculus, the derivative of y = -2.5(x-4)2 - 5 is y' = -5(x-4). Solving the equation -5(x-4) = 0 gives x = 4 (since the slope of the parabola at the vertex is zero). Plug this back into the equation: y = -2.5(4 - 4) -5 = -5, so the y-coordinate is -5. The equation of the parabola is given in the vertex form y = a(x - h)2 + k, where (h, k) is the vertex. So the vertex is (4, -5).
So you need something like this: y = a*(x - 4)² + 3. This will make the vertex be at (4,3). Then it looks like you have another point on the parabola (3,5). Plug that in and solve for a. 5 = a*(3-4)² + 3. This becomes 5 = a + 3, so a=2, then the equation is: y = 2*(x - 4)² + 3
A parabola with vertex (h, k) has equation: y = a(x - h)² + k With vertex (-3, -1) this becomes: y = a(x - -3)² + -1 = a(x + 3)² - 1 The point (4, 0) is on this parabola so: 0 = a(4 + 3)² - 1 → 7²a = 1 → a = 1/49 Thus the coefficient of x² is 1/49.
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5
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6
The coordinates will be at the point of the turn the parabola which is its vertex.
The standard equation for a Parabola with is vertex at the origin (0,0) is, x2 = 4cy if the parabola opens vertically upwards/downwards, or y2 = 4cx when the parabola opens sideways. As the focus is at (0,6) then the focus is vertically above the vertex and we have an upward opening parabola. Note that c is the distance from the vertex to the focus and in this case has a value of 6 (a positive number). The equation is thus, x2 = 4*6y = 24y
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-5
-3
-1
The given equation is not that of a parabola.