Question 2.6.7: Find the vertex of the parabola y=f(x)=-2x²-12x-13....
Find the vertex of the parabola y=f(x)=-2x²-12x-13.
Since the coefficient of x² is -2 and -2<0, the parabola opens downward and the y-value of the vertex is a maximum value. We assign -2x²-12x-13 to Y_1 \text {and graph} Y_1 in a standard viewing rectangle.
Use the left cursor key to move the blinking cursor to the left of the vertex and press \boxed {\text {ENTER}}.
Now move the cursor to the right of the vertex and press \boxed {\text {ENTER}}.
As a guess, place the cursor between the left and right bounds and press \boxed {\text {ENTER}}.
Calculator Note: Alternatively, we can enter x-values for our responses. The following responses produce a maximum of 5 at x=-3.
The calculator indicates that the vertex is about (-3, 5). (You may get different results depending on your cursor placements.)
We can also find a maximum value from the home screen as follows. (Assume we have looked at the graph and estimated that the x-coordinate of the vertex lies between -3.5 and -2.5 .) First we find the x-value of the vertex.
Next we find the y-value of the vertex using the result from fMax (it’s stored in ANS).
Notice the “strange” results given for fMax. (Your professor will not be too impressed if you say that the vertex is (-3.000001138,5).) In this case a calculator is helpful, but it is easy to calculate that
-\frac{b}{2 a}=-\frac{-12}{2(-2)}=-3 \quad \text { and } \quad f(-3)=5 \text {, }
