find the equation of a parabola that opens to the right with given vertex: (0,3) and passes through the point: (2,-1)
with a vertex of (0,3) and opening up to the right, the equation is
x = a(y-3)^2 + 0
but it passes through (2,-1)
2 = a(16)
a = 1/8
x = (1/8)(y-3)^2
or
8x = (y-3)^2
To find the equation of a parabola that opens to the right with a given vertex and passes through a point, we can use the vertex form of the equation for a parabola. The vertex form is given by:
(y - k) = a(x - h)^2
Where (h, k) is the vertex of the parabola.
In this case, the given vertex is (0,3), so h = 0 and k = 3.
Substituting these values into the equation, we have:
(y - 3) = a(x - 0)^2
(y - 3) = ax^2
Now we need to find the value of 'a'. To do this, we substitute the point (2,-1) into the equation:
(-1 - 3) = a(2^2)
-4 = 4a
Simplifying, we find that a = -1.
Substituting this value of 'a' back into the equation, we have:
y - 3 = -x^2
Therefore, the equation of the parabola that opens to the right with a vertex at (0,3) and passes through the point (2,-1) is y - 3 = -x^2.
To find the equation of a parabola that opens to the right, we need to use the general form of the equation for a parabola:
(y - k) = a(x - h)^2
Where (h, k) represents the vertex of the parabola.
Given that the vertex is at (0, 3), we substitute these values into the equation:
(y - 3) = a(x - 0)^2
(y - 3) = ax^2
Now, we need to find the value of 'a'. To do this, we use the given point (2, -1), which lies on the parabola. Substitute these values into the equation:
(-1 - 3) = a(2^2)
-4 = 4a
Solve the equation for 'a':
a = -4/4
a = -1
Now that we have the value of 'a', we substitute it back into the equation:
y - 3 = -1 * x^2
This is the equation of a parabola that opens to the right with a vertex at (0, 3) and passes through the point (2, -1).