***FAN AND MEDAL***
The second part of the new coaster is a parabola.
4)Ray needs help creating the second part of the coaster. Create a unique parabola in the pattern f(x) = ax2 + bx + c. Describe the direction of the parabola and determine the y-intercept and zeros.
5)The safety inspector notes that Ray also needs to plan for a vertical ladder through the center of the coaster's parabolic shape for access to the coaster to perform safety repairs. Find the vertex and the equation for the axis of symmetry of the parabola, showing your work, so Ray can include it in his coaster plan.

- anonymous

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- schrodinger

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- anonymous

@phi

- anonymous

oh thats simple, what do u think

- anonymous

i dont thats why im asking, im not good at math

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## More answers

- anonymous

what grade r u in

- anonymous

now im 10, but im take flvs algebra 1

- anonymous

ok

- anonymous

so read the question carefully again

- anonymous

i will help

- anonymous

thank you!!! finally!!

- anonymous

but why u ignoreing me

- anonymous

i tried to fan

- anonymous

when someone help me and give the answers, i will be fan

- anonymous

@jim_thompson5910

- anonymous

@SolomonZelman @jdoe0001

- SolomonZelman

have you chosen the parabola for question #4?

- SolomonZelman

Make up any parabola that you like, that will be convinient for you to use.
For example, i would make up the following parabola:
y=-x²+4x+5

- SolomonZelman

want to use this example, or do you want to use your own example (if you want to use your own example, then make one up)

- anonymous

i want to use your example ;/ @SolomonZelman

- anonymous

are you there @SolomonZelman

- SolomonZelman

ok, we need to find the vertex.
y=-x²+4x+5
y=-(x²-4x)+5
what number would you want
y=-(x²-4x+\(\color{red}{\rm here}\))+5
to make the expression in parenthesis a perfect square?

- anonymous

i can use number 5?

- SolomonZelman

you need to make the part inside the parenthesis into a perfect square trinomial....
do you know what a perfect square trinomial is?

- anonymous

no ;/

- SolomonZelman

you know that (x+a)² would be expanded the following way:
(x+a)² = (x+a)(x+a) = x²+ax+ax+a² = x²+2ax+a²
(do you know this?)

- anonymous

you ask me if i know how to do this?

- SolomonZelman

yes, if you followed the steps i did , and if you would be able to expand similar expressions like this on your own.

- anonymous

i see its not really hard to understand that

- SolomonZelman

ok, very good!

- SolomonZelman

So, what we have as the result, the x²+2ax+a² is called a perfect square trinomial

- SolomonZelman

this is an expression that can be factored into (x+a)²

- SolomonZelman

(of course, a is some constant, and x is the variable)

- SolomonZelman

Ok, can you expand
(x+1)² for me?

- anonymous

ok wait

- SolomonZelman

sure, take your time.

- anonymous

x (x =2) + 1
x^2 + 2x + 1
x= -1

- anonymous

its that right?

- SolomonZelman

i am trying to undertsnad line 1 and 3....

- SolomonZelman

there is a rule for this:
\(\large\color{black}{ \displaystyle (b+a)^2= b^2+2ba+a^2 }\)
and so it would be true in this case:
\(\large\color{black}{ \displaystyle (x+a)^2= x^2+2xa+a^2 }\)
and same way, we can say:
\(\large\color{black}{ \displaystyle (x+1)^2= x^2+2x(1)+(1)^2=x^2+2x+1 }\)

- SolomonZelman

(we are just expanding....)

- SolomonZelman

but an expression that is in the form of x²+2ax+a² is the "perfect square trinomial"
it is prefect square because it takes to multiply (x+a) times (x+a) to get it...

- SolomonZelman

following so far?

- anonymous

mmum yea..

- SolomonZelman

So, now lets think it backwards.

- anonymous

ok... so?

- SolomonZelman

This (below) is an example of how to find the last term for a perfect square trinomial...
Say I have \(\large\color{black}{ \displaystyle x^2+6x }\)
and I want to know what number to add
\(\large\color{black}{ \displaystyle x^2+6x+\color{red}{\rm here} }\)
to make this expression a "perfect square trinomial"
\(\rm \large Lets~~compare!\)
\(\large\color{black}{ \displaystyle x^2+6x+\color{red}{\rm here} }\) (our expression where we want to add a
number to make it a perfect square trinomial)
\(\large\color{black}{ \displaystyle x^2+2ax+a^2 }\) (the general form of a perfect square trinomial)
So you can see based on the first 2 terms of each of the expressions that the "2a" part in our case is 6.
So if 2a is 6, then a is 3, and then a² is 9.
So we would want to add 9 to make our expression a perfect square trinomial.
\(\large\color{black}{ \displaystyle x^2+6x+\color{red}{\rm 9} }\)

- SolomonZelman

And so it would always follow, that when you have:
\(\large\color{black}{ \displaystyle x^2+\color{red}{\rm c}x }\)
then the number you have to add to make the expression
into a perfect square trinomial is:
\(\large\color{black}{ \displaystyle \frac{\color{red}{\rm c} ^2}{4}}\)

- SolomonZelman

if you have a question ask.... or if you are getting it, say so...
(if you need more time to read, then keep reading)

- anonymous

@jim_thompson5910

- SolomonZelman

do i know the answer...
i don't really know the question....
what is the first part of the roller coaster, if you are asked to create the second one?

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