Quadratic Formula Lesson

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1

Quadratic Formula

Finding the Roots when Factoring isn't Possible

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Where do we get the quadratic formula?

ax^2+bx\ +c=0

4a\left(ax^2+bx+c\right)=0

4a^2x^2+4abx+4ac=0

4a^2x^2+4abx\ =-4ac

4a^2x^2+4abx+b^2=b^2-4ac

\left(2ax+b\right)^2=b^2-4ac

2ax+b=\pm\sqrt{b^2-4ac}

2ax=-b\pm\sqrt{b^2-4ac}

x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}

3

How do we use it?

First, the equation must be in standard form,
$ax^2+bx+c=0$
Next, identify a, b, and c. Substitute them into the formula.
Finally, simplify!

4

Example: $x^2+2x\ -63=0$

$x=\frac{-2\pm\sqrt{\left(2\right)^2-4\left(1\right)\left(-63\right)}}{2\left(1\right)}$

$x=\frac{-2\pm\sqrt{4+252}}{2}$

$x=\frac{\left(-2\pm16\right)}{2}$

$x=7\ or\ -9$

5

Practice

1.\ \ \ 6x^2-11x-10=0

2.\ \ \ -x^2+2x=1

3.\ \ \ -2x^2+3x=4x-15

4.\ \ \ 8x^2=10x

Quadratic Formula

Finding the Roots when Factoring isn't Possible

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