Question

Постройте график функции: y=-3^2+12x можете пожалуйста с объяснением

Answer 1

Ответ:

Объяснение:

Смотри

Answer 2

Graph of the Function y = -3x^2 + 12x

To graph the function y = -3x^2 + 12x, we can start by identifying the key components of the quadratic function. The general form of a quadratic function is y = ax^2 + bx + c, where a, b, and c are constants.

In the given function y = -3x^2 + 12x: - a = -3 (coefficient of x^2) - b = 12 (coefficient of x) - c = 0 (there is no constant term)

Key Points and Graphing Process

1. Vertex of the Parabola: The vertex of the parabola can be found using the formula: \[ x_v = \frac{-b}{2a} \] \[ y_v = f(x_v) \] where \((x_v, y_v)\) is the vertex of the parabola.

Substituting the values of a and b into the formula: \[ x_v = \frac{-12}{2*(-3)} = 2 \] \[ y_v = -3*(2)^2 + 12*(2) = 12 \]

So, the vertex of the parabola is at the point (2, 12).

2. x-intercepts: To find the x-intercepts, we set y = 0 and solve for x. These are the points where the parabola intersects the x-axis.

Setting y = 0 in the function: \[ 0 = -3x^2 + 12x \] \[ 0 = -3x(x - 4) \]

This gives us two x-intercepts at x = 0 and x = 4.

3. Axis of Symmetry: The axis of symmetry is a vertical line that passes through the vertex of the parabola. It can be found using the formula: \[ x = \frac{-b}{2a} \]

Substituting the values of a and b into the formula: \[ x = \frac{-12}{2*(-3)} = 2 \]

So, the axis of symmetry is the line x = 2.

Graph of the Function

Now, let's plot these key points and sketch the graph of the function y = -3x^2 + 12x:

- Vertex: (2, 12) - x-intercepts: (0, 0) and (4, 0) - Axis of Symmetry: x = 2

The graph is a downward-opening parabola, with the vertex at (2, 12) and x-intercepts at (0, 0) and (4, 0). The axis of symmetry is the vertical line x = 2.

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