Question

Y=-x^2-5x+6 график параболы

Answer 1

Графиком квадратичной функции является парабола, ветви которой направлены вниз, так как a = -1 < 0. Найдем координаты вершины параболы

$x=-\dfrac{b}{2a} =\dfrac{5}{2\cdot(-1)} =-2.5$

Значение абсциссы вершины параболы подставить в функцию:

$y=-(-2.5)^2-5\cdot(-2.5)+6=-6.25+12.5+6=12.25$

Таким образом, получили точку A вершины параболы, координаты которой (-2.5; 12.25).

Answer 2

To plot the graph of the parabola represented by the equation y = -x^2 - 5x + 6, we need to find points that lie on the curve and then connect them to visualize the shape of the parabola. The general form of a parabola is y = ax^2 + bx + c, where a, b, and c are constants.

Let's find a few points to plot the graph:

1. x = -3: y = -(-3)^2 - 5(-3) + 6 y = -9 + 15 + 6 y = 12

2. x = -2: y = -(-2)^2 - 5(-2) + 6 y = -4 + 10 + 6 y = 12

3. x = -1: y = -(-1)^2 - 5(-1) + 6 y = -1 + 5 + 6 y = 10

4. x = 0: y = -(0)^2 - 5(0) + 6 y = 0 + 0 + 6 y = 6

5. x = 1: y = -(1)^2 - 5(1) + 6 y = -1 - 5 + 6 y = 0

6. x = 2: y = -(2)^2 - 5(2) + 6 y = -4 - 10 + 6 y = -8

7. x = 3: y = -(3)^2 - 5(3) + 6 y = -9 - 15 + 6 y = -18

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

(Note: The x and y values are approximate due to manual plotting.)

luaCopy code
  ^ 
  |                      *
  |                   *   
12|                *     
  |             *     
10|          *     
  |       *     
  |    *    
 6| *   
  |*  
  +------------------------------------>
     -3   -2   -1    0    1    2    3   (x-axis)

The graph of the parabola y = -x^2 - 5x + 6 is a downward-opening parabola with its vertex at the point (x, y) ≈ (-1.25, 12.25). It opens downwards because the coefficient of x^2 (a) is negative. The y-intercept of the parabola is at y ≈ 6.

Please note that this is just a rough sketch, and for a more accurate representation, you can use graphing software or a graphing calculator.