Week 7 : using the quadratic formula to solve quadratic functions

This is the quadratic formula:

$\begin{array}{*{20}c} {x = \frac{{ - b \pm \sqrt {b^2 - 4ac} }}{{2a}}} & {{\rm{when}}} & {ax^2 + bx + c = 0} \\ \end{array}$

The quadratic formula is extremely useful because it can solve for x of ANY quadratic.

Ex. $x^2-7x+12=0$

Now we just plug in our a,b and c values into the quadratic formula.

${x=\frac{{ 7 \pm\sqrt{7^2 - 4(1)(12)} }}{{2(1)}}}$

${x=\frac{{ 7 \pm\sqrt{1} }}{{2}}}$

${x=\frac{{ 7 +{1} }}{{2}}}=8/2=4,$ ${x=\frac{{ 7 -{1} }}{{2}}}=6/2=3,$

Using the quadratic formula, we now know that x=3 and x=4.

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