The sign of the leading coefficient determines whether the graph has a minimum or a maximum value. Is the leading coefficient positive or negative?
Maximum Value: - 4.11
Practice makes perfect
Before we take a look at the function on a graphing calculator, notice that the equation is not in the standard form of a polynomial. To see the terms more easily, we can rewrite the equation to be in standard form.
y=28x-15-18x^2 ⇔ y=-18x^2+28x-15
We want to find the minimum or maximum value of this function. Because the leading coefficient is negative, we know we are looking for a maximum value. Now, let's draw the function on a graphing calculator. We begin by pushing the Y= button and typing the equation in the first row.
Having entered the equation in the calculator, we now push GRAPH to draw it.
Next, to find the maximum, push 2nd and TRACE. From this menu, choose maximum.
The calculator will prompt you to choose left and right bounds and to provide the calculator with a best guess of where the maximum might be.
Maximum and minimum values refer to a function's y-value. Therefore, the function's maximum y-value is about - 4.11.
