To find the quadratic function in vertex form that satisfies the given conditions, we can start with the general vertex form equation:
f(x) = a(x - h)^2 + k
Where (h, k) represents the vertex of the parabola. Given that the vertex is (4, -10), we can substitute these values into the equation:
f(x) = a(x - 4)^2 - 10
Now, let's use the additional point (-1, 5) to find the value of 'a.' Substituting these values into the equation, we get:
5 = a(-1 - 4)^2 - 10
Simplifying further:
5 = 25a - 10
Adding 10 to both sides:
15 = 25a
Dividing by 25:
a = 15/25
Simplifying:
a = 3/5
Now that we have the value of 'a,' we can substitute it back into the equation to obtain the final quadratic function in vertex form:
f(x) = (3/5)(x - 4)^2 - 10
Therefore, the quadratic function with a vertex at (4, -10) and passing through the point (-1, 5) is:
f(x) = (3/5)(x - 4)^2 - 10
