Comments and Help with standard form for quadratics worksheet
Video instructions and help with filling out and completing standard form to vertex form worksheet answer key
Instructions and Help about advanced math vertex form to standard form answers
Hi welcome to MooMooMath Today we are going
to talk about Quadratics and changing a quadratic from standard form to vertex form Lets overview
quickly what standard form is. Standard form is ax squared plus bx plus c is equal to y
and vertex is equal to a parenthesis minus h quantity squared plus k equals y. Those
are the two forms of the quadratic. The vertex form is handy because the hk is your vertex
and standard form is nice if you are using the quadratic formula. Sometimes we have to
go from standard form to vertex form . Let's learn how to do that. Let's start with a lead
coefficient of one which is the easier one. We have x^2 + 8x + 3 = y We want to change
this to the vertex form. Step 1 is to group our x values together and complete the square.so
we can write the equation as a perfect square. I will write the x^2 and 8x together. I will
push the positive 3 to the side because the constant 3 does not complete the square. What
we need to do is find a value that completes the square. I will take the value b which
is the coefficient to the linear term and half it and square it and this will complete
the square. I will take b and half it and then square it. Half of 8 is 4 and 4 squared
is 16. I will put 16 back in the equation to complete the square. What I have completed
with these three terms is a trinomial that will factor to (x+4)^2 Next I can't just add
16 to the equation because it will be unbalanced. When I add 16 it is out of balance, so I have
to subtract 16 from the equation to get it back in balance. I will group negative 16
with constant 3 and add these together to get -13. What I have done is combine those
two constants together, and now we have our quadratic in vertex form. h is -4 and k is
-13. h is always the opposite sign of what we see in the equation because it is x-h and
k is the same value which is -16. The vertex is (-4,-13)
Let's try another one so you can see the pattern. x^2 + 24x -1 = f(x)
Group the x's together x squared and 24x push the 1 over which will become part of
my k value. Part of the constant on the outside. Now complete the square, take 24 and half
it and square it So half of 24 is 12 and 12 squared is 144. We can't just 144 without
subtracting 144 . Now group the first three terms together to make our perfect square.
The perfect square it factors to is always the square root of what we just found. (the
144) and in the back we get negative 145. Now we have our functions, so we can figure out
our h and k. h is the opposite of what we see (-12) and k is the same sign as what we
see, and there is your vertex that you can use to graph your quadratic equation. Hope
this video was helpful.
