Identify a, b, and c in the given quadratic function. What does the value of a tell you about the function?
Maximum Value: 13.25 Domain: {all real numbers} Range: {f(x)|f(x)≤ 13.25}
Practice makes perfect
Let's begin by rewriting our function in the general expression of a quadratic function, y=ax^2+bx+c.
f(x) = - x^2 -7x +1⇔ f(x) = - 1x^2 + (- 7)x + 1
We can see that a = - 1, b = - 7, and c = 1.
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=- 1, 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 13.25, the range is all real numbers less than or equal to 13.25.
Domain:& {all real numbers}
Range:& {f(x)|f(x)≤ 13.25}
