Question

Решите квадратическую функцию Xв квадрате+4|x|-6 на графике должно получится что-то похожее на M

Answer 1

Решение смотри на фото

Answer 2

Solving the Quadratic Function

To graph the quadratic function \(x^2 - 4|x| - 6\), we can start by finding the x-intercepts, y-intercept, and vertex of the function.

1. Finding the x-intercepts: - The x-intercepts are the points where the graph crosses the x-axis. To find them, we set \(y = 0\) and solve for x.

2. Finding the y-intercept: - The y-intercept is the point where the graph crosses the y-axis. To find it, we set \(x = 0\) and solve for y.

3. Finding the vertex: - The vertex of the quadratic function \(ax^2 + bx + c\) is given by the formula \((-b/2a, f(-b/2a))\), where \(f(x) = ax^2 + bx + c\).

Let's proceed with these calculations.

Finding the X-Intercepts

The x-intercepts are the points where the graph crosses the x-axis. To find them, we set \(y = 0\) and solve for x.

The function \(x^2 - 4|x| - 6\) can be split into two cases for solving for x: 1. When \(x \geq 0\): \(x^2 - 4x - 6\) 2. When \(x < 0\): \(x^2 + 4x - 6\)

Finding the Y-Intercept

The y-intercept is the point where the graph crosses the y-axis. To find it, we set \(x = 0\) and solve for y.

Finding the Vertex

The vertex of the quadratic function can be found using the formula \((-b/2a, f(-b/2a))\), where \(f(x) = ax^2 + bx + c\).

Let's calculate these values to graph the function.