Exercise
Find the section in x-aixs where the line:
is below the parabla:
Final Answer
Solution
We want to find for which points in x-aixs the following inequality is true:
Move everything to one side:
It is a square inequality. Its coefficients are
The coefficient of the square expression (a) is positive, so the parabola (quadratic equation graph) “smiles” (= bowl-shaped). The sign of the inequality means we are looking for the sections the parabola is above the x-axis. We find the solutions (= zeros = roots) of the quadratic equation using the quadratic formula. Putting the coefficients in the formula gives us
Hence, we get the solutions:
Because the parabola we got “smiles” and we look for the section where it is above the x-axis, we get that the requested section is
Here are the line and the parabola:
You can see that the line is indeed below the parabola in the section we found.
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