Quadratic Solutions from Factored Form

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What is the factored form of a quadratic equation?

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The factored form of a quadratic equation is expressed as (x - p)(x - q) = 0, where p and q are the solutions of the equation.

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CCSS.HSA-REI.B.4B

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How do you find the solutions of a quadratic equation in factored form?

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To find the solutions, set each factor equal to zero: (x - p) = 0 and (x - q) = 0, then solve for x.

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CCSS.HSA-REI.B.4B

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x=0, x=7

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CCSS.HSA-REI.B.4B

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x=-1, x=8

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CCSS.HSA-REI.B.4B

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x=-1, x=9

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CCSS.HSA-REI.B.4B

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q=-\frac{1}{2}, q=9

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CCSS.HSA-REI.B.4B

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x=-6, x=-4

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CCSS.HSA-REI.B.4B

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What does it mean if a quadratic equation has two distinct real solutions?

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It means the parabola intersects the x-axis at two points.

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CCSS.HSF-IF.C.7A

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What does it mean if a quadratic equation has one real solution?

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It means the parabola touches the x-axis at one point (the vertex).

Tags

CCSS.HSF-IF.C.7A

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What does it mean if a quadratic equation has no real solutions?

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It means the parabola does not intersect the x-axis at all.

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CCSS.HSF-IF.C.7A