write a equation for each parabola.
vertex(0,1),focus(0,5)
Write this equation in standard form..
y=x2-6x+11
the x is squared
Y=2/3-1
y=-x+4
To write the equation of a parabola given its vertex and focus, we need to determine if the parabola opens upward or downward.
Since the vertex is at (0,1) and the focus is at (0,5), we can see that the parabola opens upward, because the focus is above the vertex.
The equation of a parabola that opens upward and has its vertex at point (h, k) and focus at (h, k + p) is given by:
(y - k) = (1 / (4p))(x - h)^2
In this case, the vertex is at (0,1) and the focus is at (0,5), so h = 0, k = 1, and p = 5 - 1 = 4.
Plug these values into the equation:
(y - 1) = (1 / (4 * 4))(x - 0)^2
Simplifying further:
(y - 1) = (1 / 16)x^2
Therefore, the equation of the given parabola is:
y = (1 / 16)x^2 + 1