Find the quadratic function that has the indicated vertex and whose graph passes through the given point.
Vertex: (2,3) Point: (0,2)
I do not know how to do this! Please explain!! Thank You
To find the quadratic function that has the indicated vertex and passes through the given point, we can use the vertex form of a quadratic function:
f(x) = a(x - h)^2 + k
where (h, k) represents the vertex of the parabola.
We are given the vertex as (2, 3). So, our equation becomes:
f(x) = a(x - 2)^2 + 3
Next, we substitute the coordinates of the given point (0, 2) into the equation to find the value of 'a'.
2 = a(0 - 2)^2 + 3
2 = 4a + 3
2 - 3 = 4a
-1 = 4a
a = -1/4
Now, we have the value of 'a'. Substituting it back into the equation, we get:
f(x) = (-1/4)(x - 2)^2 + 3
So, the quadratic function that has the vertex (2, 3) and passes through the point (0, 2) is:
f(x) = (-1/4)(x - 2)^2 + 3