Question

постройте график функции y=-x^2-9x-16.25

Answer 1

очевидно что это обычная парабола, т.к. коэффициент при x^2 она направлена вверх

найдем начало координат

экстремум там где производная обращается в 0, т.е. 2x-9 = 0, т.е. x = 4,5 подставив это значение в ф-ю получаем f(4,5) = -36,5

т.о. график это парабола с ветвями вверх и минимумом в точке (4,5; -36,5) строить из этой точки можно по лекалу

 

 

 

 

 

 

Answer 2

Graph of the Function y = -x^2 - 9x - 16.25

To graph the function y = -x^2 - 9x - 16.25, we can plot several points and connect them to create a smooth curve. Let's start by finding a few points on the graph.

We can choose different values for x and calculate the corresponding y values using the given equation. Here are some points:

| x | y | |---|---| | -5 | -6.25 | | -4 | -0.25 | | -3 | 5.75 | | -2 | 11.75 | | -1 | 17.75 | | 0 | 23.75 | | 1 | 29.75 | | 2 | 35.75 | | 3 | 41.75 | | 4 | 47.75 | | 5 | 53.75 |

Now, let's plot these points on a graph:


As we can see from the graph, the function y = -x^2 - 9x - 16.25 is a downward-opening parabola. The vertex of the parabola is located at the point (-4.5, -33.25). The graph intersects the x-axis at approximately x = -7.5 and x = 0.5, and it does not intersect the y-axis.

The graph is symmetric with respect to the vertical line passing through the vertex. The function has a maximum value at the vertex and decreases as x moves away from the vertex in either direction.

Please note that the graph is an approximation and may not be completely accurate.