Question

***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.

Answer 1

@phi

Answer 2

oh thats simple, what do u think

Answer 3

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

Answer 4

what grade r u in

Answer 5

now im 10, but im take flvs algebra 1

Answer 6

ok

Answer 7

so read the question carefully again

Answer 8

i will help

Answer 9

thank you!!! finally!!

Answer 10

but why u ignoreing me

Answer 11

i tried to fan

Answer 12

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

Answer 13

@jim_thompson5910

Answer 14

@SolomonZelman @jdoe0001

Answer 15

have you chosen the parabola for question #4?

Answer 16

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

Answer 17

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)

Answer 18

i want to use your example ;/ @SolomonZelman

Answer 19

are you there @SolomonZelman

Answer 20

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?

Answer 21

i can use number 5?

Answer 22

you need to make the part inside the parenthesis into a perfect square trinomial....

do you know what a perfect square trinomial is?

Answer 23

no ;/

Answer 24

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?)

Answer 25

you ask me if i know how to do this?

Answer 26

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

Answer 27

i see its not really hard to understand that

Answer 28

ok, very good!

Answer 29

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

Answer 30

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

Answer 31

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

Answer 32

Ok, can you expand
(x+1)² for me?

Answer 33

ok wait

Answer 34

sure, take your time.

Answer 35

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

Answer 36

its that right?

Answer 37

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

Answer 38

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:

\(\large\color{black}{ \displaystyle (x+1)^2= x^2+2x(1)+(1)^2=x^2+2x+1 }\)

Answer 39

(we are just expanding....)

Answer 40

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...

Answer 41

following so far?

Answer 42

mmum yea..

Answer 43

So, now lets think it backwards.

Answer 44

ok... so?

Answer 45

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.

\(\large\color{black}{ \displaystyle x^2+6x+\color{red}{\rm 9} }\)

Answer 46

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:

\(\large\color{black}{ \displaystyle \frac{\color{red}{\rm c} ^2}{4}}\)

Answer 47

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

Answer 48

@jim_thompson5910

Answer 49

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?