Question

Изобразите схематически график функции y=2x^2-3

Answer 1

Смотри в прикрепленном файле

Answer 2

Function and Graph of y = 2x^2 - 3

The function y = 2x^2 - 3 is a quadratic function, which means it is a second-degree polynomial. This type of function forms a parabola when graphed.

The general form of a quadratic function is y = ax^2 + bx + c, where a, b, and c are constants. In the given function, a = 2, b = 0, and c = -3.

To graph the function, we can use the following steps: 1. Find the vertex of the parabola using the formula (-b/2a, f(-b/2a)). 2. Find the y-intercept by substituting x = 0 into the function. 3. Find the x-intercepts (if any) by solving the equation 2x^2 - 3 = 0.

Let's proceed with these steps to graph the function.

Finding the Vertex

The x-coordinate of the vertex is given by -b/2a. In this case, since b = 0, the x-coordinate of the vertex is simply -0/2*2 = 0. To find the y-coordinate, we substitute x = 0 into the function: y = 2(0)^2 - 3 = -3.

So, the vertex of the parabola is at (0, -3).

Finding the Y-Intercept

To find the y-intercept, we substitute x = 0 into the function: y = 2(0)^2 - 3 = -3.

So, the y-intercept is at (0, -3).

Finding the X-Intercepts

To find the x-intercepts, we solve the equation 2x^2 - 3 = 0: 2x^2 = 3 x^2 = 3/2 x = ±√(3/2).

So, the x-intercepts are at (√(3/2), 0) and (-√(3/2), 0).

Graph of y = 2x^2 - 3

Now that we have the vertex, y-intercept, and x-intercepts, we can graph the function. The parabola opens upwards because the coefficient of x^2 is positive.

The graph of the function y = 2x^2 - 3 is a parabola that opens upwards, with the vertex at (0, -3) and x-intercepts at (√(3/2), 0) and (-√(3/2), 0).

I hope this helps! If you have any further questions or need additional assistance, feel free to ask.