Above is the website that we looked at on Friday to examine what effect the different variables in a quadratic equation have on its graph. Please look at this site so that you know how to predict the overall shape of the graphs!
I noticed a lot of confusion today in regards to factoring quadratics. Remember, a quadratic function is always in the form ax2 + bx + c = 0. All of the variables can be positive or negative, whole numbers or fractions, (they will always be whole numbers for this class), but our a value will never be 0. If our a term is 0, then we're left with bx + c = 0, which we recognize to be a linear function.
Because they will always be in this form (look familiar? check out the trinomials posts!) Always, always, ALWAYS check your equation first to see if you can pull out the GCF (Greatest Common Factor). Sometimes this GCF can be something subtle, like pulling out a -1, so make sure you check every time!
Once you have the GCF pulled out (if it's anything other than +1), to factor the quadratic you're just performing the same steps as you would when factoring a trinomial. If trinomials are still difficult, definitely check out the links for those pages - I tried to include both extra samples and a video example for each part!
Our roots for a quadratic equation are just our x-interepts, so when we're looking for the roots of an equation, you're going to figure out what the value(s) of x is(are) when y=0. In other words, we're trying to solve the equation for x, but we can either have 1 or 2 real number values that satisfies the equation. There is also the option of having imaginary roots, but since that is not something we need to worry about until Algebra 2, just assume I'm not mean enough to give you a problem you ABSOLUTELY CANNOT find the roots of (I promise I'm not). If you have a factored form, and it's set equal to zero, everything is ice from there.
(thing 1)*(thing 2) = 0 ---> implies that either (thing 1) = 0 OR (thing 2) = 0
With that in mind, hopefully the rest of the week will be easier to follow. We're going to go over completing the square again and do sample problems tomorrow in class.
REMEMBER: if you're stuck on something, you are always welcome to come in during lunch or after school to work one-on-one!!!
PS: I added this site to Mrs. Page's classroom webpage that you all already have access to. I'll make sure to double post any assignments or EOC help to ensure the maximum number of people
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