COLLEGE ALGEBRA: AN INVESTIGATIVE APPROACH

by

S. Kastberg & T. Barron

THE QUADRATIC FORMULA

INVESTIGATION 2: Using the descriminant to find the range of a coefficent variable

Consider the equation . For what values of b does this equation have solutions in the real numbers?

Investigate this question by looking at the graph of the descriminant of the equation. Recall that the discriminate is given by the formula . So to investigate the values of b for which the equation has solutions in the real numbers we can graph .

 

Now we can examine this graph to find the values of b for which the quadratic equation has a solutions.

Remember that the x axis for the graph are values of b and the y axis are values of d.

Now using the graph can you find values of b for which the quadratic equation has solutions?

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