Question

1) -х²-3х+10>02) у=-3х²+6х-3​

Answer 1

*К сожалению, я не знаю, как решить 2, но чем смогла, помогла

Answer 2

1. To solve the inequality -x² - 3x + 10 > 0, we can follow these steps:

Step 1: Set the inequality equal to zero: -x² - 3x + 10 = 0

Step 2: Factorize the quadratic equation: -(x - 2)(x + 5) = 0

Step 3: Find the critical points by setting each factor equal to zero: x - 2 = 0 --> x = 2 x + 5 = 0 --> x = -5

Step 4: Plot these critical points on a number line: <--------(-5)--------(2)-------->

Step 5: Choose test points within each region: For the region to the left of -5, let's choose x = -6. For the region between -5 and 2, let's choose x = 0. For the region to the right of 2, let's choose x = 3.

Step 6: Substitute the test points into the inequality: For x = -6: -(-6)² - 3(-6) + 10 = -36 + 18 + 10 = -8 For x = 0: -(0)² - 3(0) + 10 = 10 For x = 3: -(3)² - 3(3) + 10 = -9 - 9 + 10 = -8

Step 7: Determine the sign of each region: <-----(+)-------(-)-------(+)--->

Step 8: Write the final solution: The solution to the inequality -x² - 3x + 10 > 0 is x ∈ (-5, 2).

2. The equation y = -3x² + 6x - 3 represents a quadratic function in standard form. To find the vertex and the axis of symmetry of this quadratic, we can use the formula:

The x-coordinate of the vertex is given by: x = -b / (2a) The y-coordinate of the vertex is obtained by substituting the x-coordinate into the equation.

In this case, a = -3, b = 6, and c = -3. x = -6 / (2 * (-3)) = -6 / (-6) = 1 y = -3(1)² + 6(1) - 3 = -3 + 6 - 3 = 0

So, the vertex of the quadratic function y = -3x² + 6x - 3 is (1, 0), and the axis of symmetry is x = 1.