Question

У=(3-х)(х-4) постройте график функции

Answer 1

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Answer 2

Equation and Graph of the Function

The equation given is U = (3 - x)(x - 4). To understand the behavior of this function, let's simplify it first:

U = (3 - x)(x - 4) U = 3x - 12 - x^2 + 4x U = -x^2 + 7x - 12

Now, let's plot the graph of this function.

To do that, we can find the x-intercepts, y-intercept, and vertex of the parabola represented by the equation.

The x-intercepts are the points where the graph intersects the x-axis. To find them, we set U = 0 and solve for x:

0 = -x^2 + 7x - 12

We can factorize this quadratic equation:

0 = (x - 3)(x - 4)

So, the x-intercepts are x = 3 and x = 4.

The y-intercept is the point where the graph intersects the y-axis. To find it, we set x = 0:

U = -0^2 + 7(0) - 12 U = -12

So, the y-intercept is y = -12.

The vertex of the parabola can be found using the formula x = -b/2a, where a, b, and c are the coefficients of the quadratic equation. In this case, a = -1, b = 7, and c = -12:

x = -7 / (2 * -1) x = -7 / -2 x = 7/2 x = 3.5

To find the corresponding y-coordinate of the vertex, we substitute x = 3.5 into the equation:

U = -(3.5)^2 + 7(3.5) - 12 U = -12.25 + 24.5 - 12 U = 0.25

So, the vertex is (3.5, 0.25).

Now, let's plot the graph using this information:


The graph of the function U = (3 - x)(x - 4) is a downward-opening parabola that intersects the x-axis at x = 3 and x = 4. The y-intercept is y = -12, and the vertex is located at (3.5, 0.25).