Question

Составить график уравнения y=2x²-5x-3

Answer 1

Ответ прилагается в фото

Answer 2

Graph of the Equation y = 2x² - 5x - 3

To graph the equation y = 2x² - 5x - 3, we can use the standard form of a quadratic equation, which is y = ax² + bx + c. In this case, a = 2, b = -5, and c = -3.

To plot the graph, we can start by finding the vertex of the parabola. The x-coordinate of the vertex can be found using the formula x = -b / (2a), and the y-coordinate can be found by substituting the x-coordinate into the equation.

Using the values a = 2 and b = -5, we can calculate the x-coordinate of the vertex as follows:

x = -(-5) / (2 * 2) = 5 / 4 = 1.25

Substituting x = 1.25 into the equation, we can find the y-coordinate:

y = 2(1.25)² - 5(1.25) - 3 = 2(1.5625) - 6.25 - 3 = 3.125 - 6.25 - 3 = -6.125

Therefore, the vertex of the parabola is (1.25, -6.125).

To plot the graph, we can choose a few x-values, calculate the corresponding y-values using the equation, and then plot the points on a coordinate plane. We can also use the symmetry of the parabola to find additional points.

Let's choose some x-values and calculate the corresponding y-values:

- x = -2: y = 2(-2)² - 5(-2) - 3 = 2(4) + 10 - 3 = 8 + 10 - 3 = 15

- x = -1: y = 2(-1)² - 5(-1) - 3 = 2(1) + 5 - 3 = 2 + 5 - 3 = 4

- x = 0: y = 2(0)² - 5(0) - 3 = 0 - 0 - 3 = -3

- x = 1: y = 2(1)² - 5(1) - 3 = 2 - 5 - 3 = -6

- x = 2: y = 2(2)² - 5(2) - 3 = 8 - 10 - 3 = -5

Now, we can plot the points (-2, 15), (-1, 4), (0, -3), (1, -6), and (2, -5) on a coordinate plane. We can also plot the vertex (1.25, -6.125).

The graph of the equation y = 2x² - 5x - 3 will be a downward-opening parabola passing through these points.

Note: The graph of the equation y = 2x² - 5x - 3 is not provided as it requires a visual representation. It is recommended to use graphing software or a graphing calculator to plot the graph accurately.