Identify a, b, and c in the given quadratic function. What does the value of a tell you about the function?
Maximum Value: - 4.75 Domain: {all real numbers} Range: {f(x)|f(x)≤ - 4.75}
Practice makes perfect
Let's begin by rewriting our function in the general expression of a quadratic function, f(x)=ax^2+bx+c.
f(x) = 2x - 5 - 4x^2 ⇔ f(x) = (- 4)x^2 + 2x + (- 5)
We can see that a = - 4, b = 2, and c = - 5.
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=- 4, 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 - 4.75, the range is all real numbers less than or equal to - 4.75.
Domain:& {All real numbers}
Range:& {f(x)|f(x)≤ - 4.75}
