Quadratic Solutions from Factored Form

Front

What is the factored form of a quadratic equation?

Back

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.

Front

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

Back

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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Back

x=0, x=7

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Back

x=-1, x=8

Front

Back

x=-1, x=9

Front

Back

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

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Back

x=-6, x=-4

Front

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

Back

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

Front

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

Back

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

Front

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

Back

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