Question

please help me understand or see if what I did is correct will give medal.....

Answer 1

The second part of the new coaster is a parabola.

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.

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.

Create a graph of the polynomial function you created in Question 4.

Answer 2

@johnweldon1993 or @SmartyPants1111 could you help i can show you what i have gotten but not sure if it is correct or not

Answer 3

Lets see what ya got! :)

Answer 4

ok

Answer 5

i picked 3 and 6 to to create the unique parabola @johnweldon1993

Answer 6

so (x-3) (x-6) then I foiled which I got x^2-6x-3x+18 then i grouped (x^2-6x)+(-3x+18)
then factored x(x-6) +3(-x+6) then i had to get rid of the negative x so i divide by the negative so I got x(x-6) +3(x-6) so then (x+3=0) which is x=-3 (x-6=0)which is x=6 and also (x-6=0)which is x=6 then if this is correct im not sure where to go from here ..

Answer 7

anyone please help

Answer 8

Your zeros should be x=3 and x=-6 if your function is y=(x-3)(x+6)

Answer 9

If you wrote the parabola as (x-3)(x-6), then you don't need to look for the zeros. You have them directly \( (x- \3) (x- \6) \). They would be 3 and 6. For the y-intercept, put x=0 and solve for y.

Answer 10

This might help : https://www.desmos.com/calculator/7lypwvbqle

Answer 11

Im not understanding what I did wrong though did i do to many steps @math&ing001

Answer 12

this is what I got

Answer 13

The whole process is messing up your result. The goal from doing all that work is to get the zeros by obtaining a factored result like (x-a)(x-b) which YOU ALREADY HAVE from the beginning. So why go through all that again. It's pointless.

Answer 14

I guess i just need to go from the beginning ...Ray needs help creating the second part of the coaster. Create a unique parabola in the pattern f(x) = ax2 + bx + c.

Answer 15

.Ray needs help creating the second part of the coaster. Create a unique parabola in the pattern f(x) = ax^2 + bx + c.

Answer 16

So you need to need foil it (x-3)(x-6) = x^2-6x-3x+18 = x^2-9x+18

Answer 17

ok i understand that

Answer 18

So what's the next step ?

Answer 19

find the y intercept

Answer 20

by setting the funtion to 0 @math&ing001 not really sure

Answer 21

Yeah just setting x to zero, then solving for y

Answer 22

so x^2-9x+18 =0^2-9(0)+18 so F(0)=18

Answer 23

Yep, so the y-intercept would be 18

Answer 24

cool so now....Describe the direction of the parabola and determine the y-intercept and zeros. ok i have the y- intercept

Answer 25

Scroll up, you also have the zeros ;-]
As for the direction in this case, it just depends on the sign of "a" in ax^2+bx+c :

Answer 26

ok so x-3=0 x=3 and x-6=0 so x=6 and because the a is positive it goes up?

Answer 27

Right !

Answer 28

awesome.. so to get the vertex is from when i graph so it would be 4.5

Answer 29

Yes, but you could also get it by derivating the function and puting it to zero :
f'(x)=2x-9=0 => x=9/2=4.5

Answer 30

oh i did not know that thank you and the axis of symmetry is that this formula x=-b/2a

Answer 31

Yep, correct !

Answer 32

A is equal to 1 and B is equal to 9 would that be equal to 4.5 like the the vertex?

Answer 33

Yes !

Answer 34

Thank you so much i think ive got it all

Answer 35

Welcome !