Question

Постройте график функций y=-3x^2-5x+2

Answer 1

$y=-3x^2-5x+2$ это уравнение параболы,
ветви вниз,
вершина: $x_0=- \frac{b}{2a}= -\frac{-5}{-6}=-\frac{5}{6};$
$y_0=-3(-\frac{5}{6})^2-5(-\frac{5}{6})+2=- \frac{25}{12}+ \frac{25}{6}+2= \frac{25}{12}+2=4\frac{1}{12}$
Точки пересечения с осью ОХ: $y=0;$  $-3x^2-5x+2=0;$
$D=49;x_1= \frac{1}{3};x_2=-2;$

Answer 2

Graph of the Function y = -3x^2 - 5x + 2

To graph the function y = -3x^2 - 5x + 2, we can plot several points and connect them to form a smooth curve. Alternatively, we can use the properties of the quadratic function to determine the shape of the graph.

The general form of a quadratic function is y = ax^2 + bx + c, where a, b, and c are constants. In this case, a = -3, b = -5, and c = 2.

To find the vertex of the parabola, we can use the formula x = -b/2a. Plugging in the values, we get:

x = -(-5) / (2 * -3) = 5/6

Substituting this value back into the equation, we can find the y-coordinate of the vertex:

y = -3(5/6)^2 - 5(5/6) + 2 = -25/12 - 25/6 + 2 = -25/12 - 50/12 + 24/12 = -51/12 = -17/4

Therefore, the vertex of the parabola is (5/6, -17/4).

To determine the shape of the graph, we can look at the coefficient of x^2, which is -3. Since the coefficient is negative, the parabola opens downwards.

Now, let's plot some additional points to get a better understanding of the graph.

When x = 0: y = -3(0)^2 - 5(0) + 2 = 2 So, we have the point (0, 2).

When x = 1: y = -3(1)^2 - 5(1) + 2 = -3 - 5 + 2 = -6 So, we have the point (1, -6).

When x = -1: y = -3(-1)^2 - 5(-1) + 2 = -3 + 5 + 2 = 4 So, we have the point (-1, 4).

Using these points, we can plot the graph of the function y = -3x^2 - 5x + 2.


Please note that the graph is a downward-opening parabola with its vertex at (5/6, -17/4). The points (0, 2), (1, -6), and (-1, 4) are also plotted on the graph.