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anonymous
 one year ago
***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 yintercept 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
 one year ago
***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 yintercept 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.

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh thats simple, what do u think

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i dont thats why im asking, im not good at math

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0now im 10, but im take flvs algebra 1

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so read the question carefully again

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0thank you!!! finally!!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0but why u ignoreing me

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0when someone help me and give the answers, i will be fan

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@SolomonZelman @jdoe0001

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0have you chosen the parabola for question #4?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0Make 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
 one year ago
Best ResponseYou've already chosen the best response.0want 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
 one year ago
Best ResponseYou've already chosen the best response.0i want to use your example ;/ @SolomonZelman

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0are you there @SolomonZelman

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0ok, we need to find the vertex. y=x²+4x+5 y=(x²4x)+5 what number would you want y=(x²4x+\(\color{red}{\rm here}\))+5 to make the expression in parenthesis a perfect square?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0you need to make the part inside the parenthesis into a perfect square trinomial.... do you know what a perfect square trinomial is?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0you 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
 one year ago
Best ResponseYou've already chosen the best response.0you ask me if i know how to do this?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0yes, if you followed the steps i did , and if you would be able to expand similar expressions like this on your own.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i see its not really hard to understand that

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0So, what we have as the result, the x²+2ax+a² is called a perfect square trinomial

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0this is an expression that can be factored into (x+a)²

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0(of course, a is some constant, and x is the variable)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0Ok, can you expand (x+1)² for me?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0sure, take your time.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0x (x =2) + 1 x^2 + 2x + 1 x= 1

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0i am trying to undertsnad line 1 and 3....

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0there 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
 one year ago
Best ResponseYou've already chosen the best response.0(we are just expanding....)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0but 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
 one year ago
Best ResponseYou've already chosen the best response.0following so far?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0So, now lets think it backwards.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0This (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
 one year ago
Best ResponseYou've already chosen the best response.0And 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
 one year ago
Best ResponseYou've already chosen the best response.0if you have a question ask.... or if you are getting it, say so... (if you need more time to read, then keep reading)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0do 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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