Hi everyone, so for this lesson I'm going
to be doing an introduction to the
quadratic formula and using Sanger
Unified's curriculum, that is unit 4
module 9 of Math 2. Also this lesson
covers two common core standards which I
listed here. So now it looks like we're
ready to jump into the lesson. So we know
from our previous knowledge that a
quadratic polynomial is of the form ax
squared plus bx plus c where a, b and c
are real numbers and x is our variable.
But, what if we set this polynomial equal
to zero? Now, we have an equation where we
have to solve for x and one way to do
that is using the quadratic equation. The
quadratic equation, or quadratic formula,
is given by this formula here. So, given
any quadratic polynomial, if we want to
solve for x, we can simply do so by using
this formula and we already know what a,
b and c are from the original polynomial
that we're given. So, we can just plug
those values into this formula. Now, let's
try out an example together. Consider the
equation 2x squared minus 8x minus 24 equals 0.
Because we know the structure of a
polynomial, we know that in this case a
equals 2, b equals negative 8 and c
equals negative 24, so now we can use the
quadratic formula to solve for x. So, we
have that x equals minus a negative 8
plus or minus the square root of
negative 8 squared minus 4 times 2 times
negative 24 all over 2 times 2. So
simplifying that we get that x equals 8
plus or minus the square root of 64
minus a negative 192 over 4. Simplifying
it a little more,
we get that x equals 8 plus or minus
square root of 256 over 4. So, finally,
since we know that the square root of
256 is 16, we get that x equals either 8
plus 16 over 4 or 8 minus 16 over 4 and
those simplify to 6 and negative 2.
Here's a few more equations for you guys
to solve using the quadratic equation
and that's all for today. Thanks guys!
