Determine whether the quadratic function shown below has a minimum or maximum, then determine the minimum or maximum value of the function
f(x)=−3(x+5) 2+5
The given quadratic function is in vertex form, f(x) = a(x-h)^2 + k, where (h, k) is the vertex of the parabola. In this case, the vertex form is f(x) = -3(x+5)^2 + 5.
The coefficient "a" is -3, which is negative, indicating that the parabola opens downwards. Therefore, the function has a maximum.
The vertex of the parabola is (-5, 5). Since the parabola opens downwards, the maximum value of the function is k = 5.
Therefore, the quadratic function has a maximum of 5.