Question

X^2+3x+2 график функций ​

Answer 1

y=x^2+3x+2

m=-b/2a=-3/2=-1,5

n=(-1,5)^2+3(-1,5)+2=-0,25

вершины точки параболы: (-1,5;-0,25)

x^2+3x+2=0

x1=-2. x2=-1

нули функции -2. -1.

x. -3. 0

y. 2. 2

Answer 2

To plot the graph of the function $f(x) = x^2 + 3x + 2$, we'll need to determine how the function behaves for various values of $x$. Here's the step-by-step process to draw the graph:

1. Identify the vertex: The vertex of the quadratic function $f(x) = ax^2 + bx + c$ is given by $(-b/2a, f(-b/2a))$. In this case, $a = 1$, $b = 3$, and $c = 2$. So, the vertex can be found as follows: $x_{\text{vertex}} = \frac{-b}{2a} = \frac{-3}{2(1)} = -\frac{3}{2} = -1.5$ $f(-1.5) = (-1.5)^2 + 3(-1.5) + 2 = 2.25 - 4.5 + 2 = -0.25$ So, the vertex is at $(-1.5, -0.25)$.

2. Find the y-intercept: The y-intercept is the point where the graph intersects the y-axis ($x = 0$). To find it, plug in $x = 0$ into the function: $f(0) = 0^2 + 3(0) + 2 = 2$ So, the y-intercept is at $(0, 2)$.

3. Find the x-intercepts (if any): The x-intercepts are the points where the graph intersects the x-axis ($y = 0$). To find them, set $f(x) = 0$ and solve for $x$: $x^2 + 3x + 2 = 0$ This quadratic equation can be factored as $(x + 1)(x + 2) = 0$, giving us two x-intercepts: $x = -1$ and $x = -2$.

Now, let's plot these points and sketch the graph:

scssCopy code
       |
       |
       |    * (vertex: -1.5, -0.25)
       |
       |
       |         * (x-intercept: -2, 0)
       |
       |
       |  * (y-intercept: 0, 2)
       |
_______|______________________
       |         |         |
      -3        -2        -1       0        1        2        3

The graph of the function $f(x) = x^2 + 3x + 2$ will be a parabola opening upwards, passing through the points we found above. It will look similar to a "U" shape with the vertex at $(-1.5, -0.25)$ and the x-intercepts at $(-1, 0)$ and $(-2, 0)$.

Please note that this is a hand-drawn sketch and not a precise graph. For a more accurate representation, you can use graphing tools or software.