We want to find the minimum or maximum value of the given function.

y = - 9 x^{2} - 12 x + 19

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.

For this function, we cannot see the maximum value in the standard viewing window. We can resize our window by pushing $WINDOW,$ changing the settings, and once more pushing $GRAPH .$ Note that the constant is $19,$ so this is the $y -$ intercept. Recognizing this gives us an idea of how high our window should go.

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 $23 .$

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