Question

Построить график функции y=x²-2x -3

Answer 1

Y=x²-2x-3=(x-1)²-4
Строим параболу у=х²
Сдвигаем ось оу на 1 влево
Сдвигаем ось ох на 4 единицы вверх
Получили параболу с вершиной в точке (1;-4),ветви вверх,точки пересечения с осями (-1;0);(3;0);(0;-3)

Answer 2

Graph of the Function y = x² - 2x - 3

To graph the function y = x² - 2x - 3, we can plot several points and connect them to form a curve. Alternatively, we can use the equation to find the vertex and the x-intercepts of the parabola.

To find the vertex of the parabola, we can use the formula x = -b/2a, where a, b, and c are the coefficients of the quadratic equation. In this case, a = 1, b = -2, and c = -3. Plugging these values into the formula, we get:

x = -(-2) / (2 * 1) = 2 / 2 = 1

So the x-coordinate of the vertex is 1. To find the y-coordinate, we substitute this value back into the equation:

y = (1)² - 2(1) - 3 = 1 - 2 - 3 = -4

Therefore, the vertex of the parabola is (1, -4).

To find the x-intercepts, we set y = 0 and solve for x:

0 = x² - 2x - 3

Factoring the quadratic equation, we have:

0 = (x - 3)(x + 1)

Setting each factor equal to zero, we get:

x - 3 = 0 --> x = 3 x + 1 = 0 --> x = -1

So the x-intercepts of the parabola are x = 3 and x = -1.

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

- Vertex: (1, -4) - X-intercepts: (3, 0) and (-1, 0)

We can also find the axis of symmetry, which is a vertical line passing through the vertex. In this case, the axis of symmetry is x = 1.

Now, let's plot the graph of the function y = x² - 2x - 3:


Please note that the graph is a downward-opening parabola, with the vertex at (1, -4), and the x-intercepts at (3, 0) and (-1, 0).

I hope this helps! Let me know if you have any further questions.