Question

X^2-3x-18<0 + график​

Answer 1

Ответ:

напирмер должен быть так

Answer 2

To graph the quadratic inequality x^2 - 3x - 18 < 0, we can start by finding the x-intercepts and the vertex of the corresponding quadratic equation x^2 - 3x - 18 = 0.

First, let's find the x-intercepts by setting the equation equal to zero:

x^2 - 3x - 18 = 0

To factorize the quadratic equation, we need to find two numbers whose product is -18 and whose sum is -3. These numbers are -6 and 3:

(x - 6)(x + 3) = 0

Now, we can set each factor equal to zero and solve for x:

x - 6 = 0 -> x = 6 x + 3 = 0 -> x = -3

So, the x-intercepts are x = 6 and x = -3.

Next, let's find the vertex of the parabola. The x-coordinate of the vertex can be found using the formula:

x = -b / (2a)

In this case, a = 1 and b = -3, so:

x = -(-3) / (2 * 1) = 3 / 2 = 1.5

To find the y-coordinate of the vertex, we substitute x = 1.5 into the quadratic equation:

y = (1.5)^2 - 3(1.5) - 18 = 2.25 - 4.5 - 18 = -20.25

Therefore, the vertex is (1.5, -20.25).

Now, we can plot these points on a graph and determine the region where the quadratic inequality x^2 - 3x - 18 < 0 is true.

Here's a rough sketch of the graph:

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     | x             x
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The x-intercepts are located at x = 6 and x = -3, and the vertex is at (1.5, -20.25). The parabola opens upward since the coefficient of x^2 is positive.

To determine the region where x^2 - 3x - 18 < 0 is true, we look for the values of x that fall below the x-axis (i.e., the region between the x-intercepts). In this case, it is the region between x = -3 and x = 6, excluding the endpoints.

Therefore, the solution to the quadratic inequality is -3 < x < 6.