Question

Решите неравенства с помощью графика соответствующей квадратичной функции 1)x^2-3x-4>0 2)-x^2-3x+4<=0 3)x^2+7x+10<0 4)-x^2+3x-2>=0и если можно на листочке написать плиз срочно

Answer 1

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Answer 2

Solving Quadratic Inequalities Using Graphs

Let's solve the given quadratic inequalities using the corresponding graphs of the quadratic functions.

1. Solving x^2 - 3x - 4 > 0: - The quadratic function is in the form of \(y = x^2 - 3x - 4\). - To find the solution, we need to determine the x-values for which the function is greater than 0.

2. Solving -x^2 - 3x + 4 <= 0: - The quadratic function is in the form of \(y = -x^2 - 3x + 4\). - We'll find the x-values for which the function is less than or equal to 0.

3. Solving x^2 + 7x + 10 < 0: - The quadratic function is in the form of \(y = x^2 + 7x + 10\). - We'll determine the x-values for which the function is less than 0.

4. Solving -x^2 + 3x - 2 >= 0: - The quadratic function is in the form of \(y = -x^2 + 3x - 2\). - We'll find the x-values for which the function is greater than or equal to 0.

Let's solve each of these inequalities using the corresponding graphs of the quadratic functions.

Graphical Solutions

1. Solving x^2 - 3x - 4 > 0: - The graph of the function \(y = x^2 - 3x - 4\) is a parabola that opens upwards. We need to find the x-values for which the function is greater than 0. - The solutions can be found by identifying the x-values where the graph is above the x-axis.

2. Solving -x^2 - 3x + 4 <= 0: - The graph of the function \(y = -x^2 - 3x + 4\) is a parabola that opens downwards. We'll determine the x-values for which the function is less than or equal to 0. - The solutions can be found by identifying the x-values where the graph is below or touching the x-axis.

3. Solving x^2 + 7x + 10 < 0: - The graph of the function \(y = x^2 + 7x + 10\) is a parabola that opens upwards. We'll determine the x-values for which the function is less than 0. - The solutions can be found by identifying the x-values where the graph is below the x-axis.

4. Solving -x^2 + 3x - 2 >= 0: - The graph of the function \(y = -x^2 + 3x - 2\) is a parabola that opens downwards. We'll find the x-values for which the function is greater than or equal to 0. - The solutions can be found by identifying the x-values where the graph is above or touching the x-axis.

Let's proceed to solve each inequality graphically and provide the corresponding solutions.