Let's begin by rewriting our function in the general expression of a quadratic function, f(x)=ax^2+bx+c.
f(x) = - 3/5x^2 +4x-8 ⇔ f(x) = - 3/5x^2 + 4x + (- 8)
We can see that a = - 35, b = 4, and c = - 8.
Determining Maximum or Minimum Value
Before we determine the maximum or minimum recall that, if a>0, the parabola has a minimum value. Conversely, if a<0, the parabola has a maximum value.
In the given function, we have a=- 35, which is less than 0. Thus, the parabola will have a maximum value.
Finding the Maximum or Minimum Value
The minimum or maximum value of a parabola is always the y-coordinate of the vertex. We can find it by first looking for the x-coordinate of the vertex, - b2a.
Unless there is a specific restriction given in the context of the problem, the domain of a quadratic function is all real numbers. In this case, there is no restriction on the value of x. Since the maximum value of the function is - 43, the range is all real numbers less than or equal to - 43.
Domain:& {all real numbers}
Range:& {f(x)|f(x)≤ - 43}
