Question

Построить график функций по алгоритму.y=x(в квадрате)-2х-3 Очень нужно помогитееее!!!

Answer 1

Итак, начнёт с того, что данная функция - квадратичная, а, значит, что график - парабола :)))
1) Ветви направлены вверх, т.к. x>0
2) Ищем точки пересечения с осью Ох: х^2-2x-3=0
Дискриминант (D) = 4 - 4*1* (-3) = 4+12 = 16
Ищем точки пересечения (корни уравнения) 
получаем, что х1= -1, а х2 = 3
3) Ищем точки пересечения с осью оу: 0^2 - 2*0 - 3 = -3
4) Находим х (вершины) = 2/2 = 1
5) Находим у (вершины) = 1^2 - 2*1 - 3= -4

Дальше строишь параболу. Получается что-то вроде этого:

Answer 2

Building a Graph for the Function y = x^2 - 2x - 3

To graph the function y = x^2 - 2x - 3, we can follow a step-by-step process to plot the points and visualize the graph.

1. Determine Key Points: - We can start by finding the vertex, y-intercept, and x-intercepts of the function.

2. Finding the Vertex: - The x-coordinate of the vertex can be found using the formula x = -b / (2a), where a is the coefficient of the x^2 term, and b is the coefficient of the x term. - Once we have the x-coordinate of the vertex, we can find the corresponding y-coordinate by substituting the x-value into the function.

3. Finding the y-intercept: - The y-intercept occurs when x = 0. We can substitute x = 0 into the function to find the y-intercept.

4. Finding the x-intercepts: - The x-intercepts occur when y = 0. We can solve the quadratic equation x^2 - 2x - 3 = 0 to find the x-intercepts.

5. Plotting the Graph: - Once we have the key points, we can plot them on a graph and connect them to visualize the shape of the parabola.

Key Points:

- Vertex: To find the vertex, we can use the formula x = -b / (2a), where a = 1 and b = -2. - y-intercept: Substitute x = 0 into the function to find the y-intercept. - x-intercepts: Solve the quadratic equation x^2 - 2x - 3 = 0 to find the x-intercepts.

Graphing the Function:

- Vertex: Using the formula, we find the x-coordinate of the vertex to be x = 1. Substituting this into the function gives us y = -4. - y-intercept: When x = 0, y = -3. - x-intercepts: Solving the quadratic equation x^2 - 2x - 3 = 0 gives us x = -1 and x = 3.

Now, let's plot these points and connect them to visualize the graph of the function y = x^2 - 2x - 3.