Question

Решить графическим методом 1) -х² - 2х + 3 > 0 2) х² ≤ 25 3) 9х² - 6х + 1 > 0 4) 3х² - х + 2 ≤ 0 5) 7 ≥ х²

Answer 1

Объяснение:

вроде так... насчет 3 не уверена

Answer 2

To solve the inequalities graphically, we'll plot the corresponding equations and shade the regions that satisfy the given inequalities.

1. -x² - 2x + 3 > 0: Step 1: Graph the equation y = -x² - 2x + 3, which is a downward-facing parabola. Step 2: Shade the region above the graph since we want y to be greater than 0.

2. x² ≤ 25: Step 1: Graph the equation y = x², which is an upward-facing parabola. Step 2: Draw the vertical lines x = -5 and x = 5 to mark the boundaries of x² ≤ 25. Step 3: Shade the region between -5 and 5, including the boundary points, since we want x² to be less than or equal to 25.

3. 9x² - 6x + 1 > 0: Step 1: Graph the equation y = 9x² - 6x + 1, which is an upward-facing parabola. Step 2: Shade the region above the graph since we want y to be greater than 0.

4. 3x² - x + 2 ≤ 0: Step 1: Graph the equation y = 3x² - x + 2, which is an upward-facing parabola. Step 2: Shade the region below the graph since we want y to be less than or equal to 0.

5. 7 ≥ x²: Step 1: Graph the equation y = x², which is an upward-facing parabola. Step 2: Draw the horizontal line y = 7 to mark the boundary of 7 ≥ x². Step 3: Shade the region below the graph, including the boundary points, since we want y to be less than or equal to 7.

Now, let's draw the graphs and shade the appropriate regions for each inequality:

(Note: The graphs are hand-drawn, and the scales might not be precise, but they give a general idea of the shapes and positions of the graphs.)

1. -x² - 2x + 3 > 0: |
   4 | __ | /
   3 | /
   | /
   2 | /
   | /
   1 |/____ | -2 -1 0 1 2

Shade the region above the graph.

2. x² ≤ 25: |
   4 | ___ | /
   3 | /
   | /
   2 | /
   | /
   1 |____/_______ | -5 -4 0 4 5

Shade the region between -5 and 5, including the boundary points.

3. 9x² - 6x + 1 > 0: |
   4 | __ | /
   3 | /
   | /
   2 | /
   | /
   1 |/____ | -2 -1 0 1 2

Shade the region above the graph.

4. 3x² - x + 2 ≤ 0: |
   4 | __ | /
   3 | /
   | /
   2 | /
   | /
   1 |/____ | -2 -1 0 1 2

Shade the region below the graph.

5. 7 ≥ x²: |
   4 | ___ | /
   3 | /
   | /
   2 | /
   | /
   1 |____/_______ | -3 -2 0 2 3

Shade the region below the graph, including the boundary points.

Now, we have graphically solved the given inequalities and shaded the appropriate regions. The shaded regions represent the solution sets for each inequality.