taylor rodriguez reflection 10 may 2010

soving and sketching parabolas

write this in your notes as you see it posted. it should help your graphing problem.

**#1
you need to see if the parabola will open up or down. think of it this was: if the first thing you see in the equation is a negative sign relate that to which way negative numbers go on a graph or think "if some thing is negative you get a thumbs down" like wise "if something is positive it gets a thumbs up"

so first thing you see at the front of the equation is a negative sign? thumbs down therefore the parabola opens down. If the first thing you see is a positive number? thumbs up therefore the parabola opens up.

(using analogies like this is good for memory. If you start thinking in terms of analogies you get faster at retaining information)

**#2
deciding the number of X intercepts is also an easy remembering problem to fix.
first you need to answer the problem

bsquared - 4(a)(c)

as you said you are very good at plugging in this formula because you have remembered it well.
look at your answer to that and

remember: positive answer is two x intercepts
negative answer is none
zero for an answer is one X intercept

its better to have two than none
so POSITIVE thing to have TWO
NEGATIVE thing to have NONE

(i dont have a trick to remember zero.. i think its just a process of elimination thing.. if i didnt get a positive answer or a negative anser that means its not two x intercepts nor is it no X intercepts,, well that means its one X intercept)

**#3
to find an x intercept you solve for X

it says that in your question

"find X intercept"
remember "find X"

(dont forget to put answer into point form. when solving for x you will always wind up having to square root. you know this meas the answer will be +/-. be sure to show this when convertine to point form. {I.E. (#,0) & (-#,0)} in many of the problems we had there was also a matter of carring a number to the other side. this is no big deal you just tack it on also. for example... if you ended with

X-2= +/- square root 6/2

you would add 2 to both sides and put in point form. therefore you'd have
(squareroot 6/2+2,0) & (- squareroot 6/2+2,0))


**#4
y- intercept is just taking the 0 in the y spot for the last answer and plugging it into the x spot in the equation. which then leaves you only the Y variable to solve for.

Remember: "Find Y intercept"
"find Y"

common sense will tell you the only way to do that is to plug something into the X spot.. and i told you what to plug in

**#5
Axis of semmatry is a simple conversion formula you'll have to memorize the same way you did for the quadratic formula. by writing it down everytime you solve for axis of semmatry until you see the formula in your sleep.

the Formula (in case it isnt written down) is

X= -b/2(a)
(the a and b plug ins of course come from the original equation)

your answer will be the point to put your DOTTED LINE on. because this formula solves for X you know it will pass through that point on the X line. You also know its a vertical line. so no worries.

**#6
the vertex is also just a matter of plugging in
remember this step follows the step ahead of it so it retains the answer for X

that means half of your vertex is solved
you already have your X point for the vertex answer

that answer is also plugged into the original equation which again leaves you to solve for y.

this means you now have your vertex point
because you solved for X in step 5
and your answer after plugging that in gave you the Y

FINALLY! now that you have turned everything into points its just a matter of locating them and marking them all on your graph.

After each point is marked connect the dots.

just as a quick check look back and see if your parabola is supposed to open up or down if your graph matches then

congratulations! everything seems to have gone
well.i know everything i've given you is alot to remember. just write down the hints and keep the sheet as a reference. it doesnt have to be word for word. just putting "step one- opens up or down? work {b-4ac} *positive thumbs up *negative thumbs down"

reading and rereading tricks to help you remember will pay off i promise

i need help on finding inverses like those is chapter four