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Perplex
Perplex
Dashboard
Topics
Exponents & LogarithmsApproximations & ErrorSequences & SeriesCounting & BinomialsProof and Reasoning
Cartesian plane & linesQuadraticsFunction TheoryTransformations & asymptotes
2D & 3D GeometryTrig equations & identities
ProbabilityDescriptive StatisticsBivariate StatisticsDistributions & Random Variables
DifferentiationIntegration
Review VideosFormula BookletMy Progress
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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:


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.

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:


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.