find the equation of a parabola that has a vertex of (-2,-3) and contains the point (4,1).
you already know the equation must be
y = a(x+2)^2 - 3
All that is missing is the value of a
To find a, plug in the given point and solve for a.
Rewrite my equation and you are all done.
To find the equation of a parabola with a given vertex and a point, you can use the vertex form of the parabola equation:
y = a(x - h)^2 + k
where (h, k) represents the coordinates of the vertex. In this case, the vertex is (-2, -3). Substituting these values into the equation, we have:
y = a(x - (-2))^2 + (-3)
y = a(x + 2)^2 - 3
To solve for the value of 'a,' we can use the point (4, 1) that the parabola contains. Substituting these coordinates into the equation, we get:
1 = a(4 + 2)^2 - 3
1 = a(6)^2 - 3
1 = 36a - 3
36a = 4
a = 4/36
a = 1/9
Now we have the value of 'a,' we can substitute it back into the equation to get the final equation of the parabola:
y = (1/9)(x + 2)^2 - 3
Therefore, the equation of the parabola is y = (1/9)(x + 2)^2 - 3.