Question

Y=-x²+4xквадратичная функция помогите пожалуйста ​

Answer 1

Ответ:

Пошаговое объяснение:

Answer 2

Ответ:

x1=0, x2=4

Пошаговое объяснение:

y=-x²+4x

0=-x²+4x

-x²+4x=0

-x (x-4)=0

x=0; x-4=0

x=0; x=4

Answer 3

Quadratic Function: y = -x² + 4x

The given function is a quadratic function in the form of y = -x² + 4x. Let's break down the function and understand its properties.

1. Coefficient of x²: The coefficient of x² is -1, which means the parabola opens downwards.

2. Coefficient of x: The coefficient of x is 4, which determines the direction and steepness of the parabola.

3. Constant term: There is no constant term in the given function.

Graph of the Quadratic Function

To visualize the graph of the quadratic function y = -x² + 4x, we can plot some points and draw a smooth curve connecting them.

Let's find the x-intercepts and the vertex of the parabola:

1. X-intercepts: To find the x-intercepts, we set y = 0 and solve for x. In this case, we have:

0 = -x² + 4x

Factoring out x, we get:

0 = x(-x + 4)

So, either x = 0 or -x + 4 = 0.

From the second equation, we find:

-x + 4 = 0 x = 4

Therefore, the x-intercepts are x = 0 and x = 4.

2. Vertex: The vertex of a quadratic function can be found using the formula x = -b / (2a), where a and b are the coefficients of x² and x, respectively.

In this case, a = -1 and b = 4. Substituting these values into the formula, we get:

x = -4 / (2 * -1) x = -4 / -2 x = 2

To find the corresponding y-coordinate, we substitute x = 2 into the function:

y = -(2)² + 4(2) y = -4 + 8 y = 4

Therefore, the vertex of the parabola is (2, 4).

Graph of the Quadratic Function

Now, let's plot the points we found and draw the graph of the quadratic function y = -x² + 4x:

- X-intercepts: (0, 0) and (4, 0) - Vertex: (2, 4)

Here is the graph:


Conclusion

In conclusion, the quadratic function y = -x² + 4x is a downward-opening parabola with x-intercepts at (0, 0) and (4, 0), and a vertex at (2, 4). The graph of the function forms a smooth curve.