To use the Quadratic Formula for graphing inequalities, follow these simple steps:
Identify the Inequality: Write down your quadratic inequality, like this: ( ax^2 + bx + c < 0 ).
Find Roots: Use the Quadratic Formula to calculate the roots. The formula looks like this:
[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ]
This will help you find the points where the graph crosses the x-axis.
Test Intervals: After you find the roots, you will have different sections or intervals on the x-axis. Pick some test points from each interval to see if they make the inequality true or false.
Graph: Draw the quadratic function on a graph. The parts where the graph is below or above the x-axis show where your inequality holds true.
Solution Representation: Write the solutions in interval notation. For example, if you found that ( ax^2 + bx + c < 0 ), you might write your answer as ( (r_1, r_2) ).
To use the Quadratic Formula for graphing inequalities, follow these simple steps:
Identify the Inequality: Write down your quadratic inequality, like this: ( ax^2 + bx + c < 0 ).
Find Roots: Use the Quadratic Formula to calculate the roots. The formula looks like this:
[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ]
This will help you find the points where the graph crosses the x-axis.
Test Intervals: After you find the roots, you will have different sections or intervals on the x-axis. Pick some test points from each interval to see if they make the inequality true or false.
Graph: Draw the quadratic function on a graph. The parts where the graph is below or above the x-axis show where your inequality holds true.
Solution Representation: Write the solutions in interval notation. For example, if you found that ( ax^2 + bx + c < 0 ), you might write your answer as ( (r_1, r_2) ).