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  • Perplex

    Quadratics (Lesson 2/2)

    Applications of Quadratics

    1 / 14

    Discussion

    We've previously learned that the solutions to a quadratic equation, ax2+bx+c=0 can always be found using the quadratic formula:

    x=2a−b±√b2−4ac​​


    But what if a parabola doesn't intersect the x-axis at all? What if it intersects only once? Examine the following parabola:


    Powered by Desmos

    How many real solutions do you see?

    Solution:

    The number of real solutions is the same as the number of times the parabola meets the x-axis.


    From the graph we see it does not intersect the x-axis at all, so there are no real roots.