Question

i need help really bad, i will fan and medal!

Answer 1

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.

f(x)=x^4+2x+8

Answer 2

@Fifciol @goodday @Minimooe @Anaise

Answer 3

did you mean to write this?

f(x) = x^2+2x+8

Answer 4

no

Answer 5

i mean im not sure...

Answer 6

The first part of Ray and Kelsey's roller coaster is a curved pattern that can be represented by a polynomial function.

Ray and Kelsey are working to graph a third-degree polynomial function that represents the first pattern in the coaster plan. Ray says the third-degree polynomial has 4 intercepts. Kelsey argues the function can have as many as 3 zeros only. Is there a way for the both of them to be correct? Explain your answer.

Kelsey has a list of possible functions. Pick one of the g(x) functions below and then describe to Kelsey the key features of g(x), including the end behavior, y-intercept, and zeros.
g(x) = x3 − x2 − 4x + 4
g(x) = x3 + 2x2 − 9x − 18
g(x) = x3 − 3x2 − 4x + 12
g(x) = x3 + 2x2 − 25x − 50
g(x) = 2x3 + 14x2 − 2x − 14

Create a graph of the polynomial function you selected from Question 2.

Part B

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.

Part C

Now that the curve pieces are determined, use those pieces as sections of a complete coaster. By hand or by using a drawing program, sketch a design of Ray and Kelsey's coaster that includes the shape of the g(x) and f(x) functions that you chose in the Parts A and B. You do not have to include the coordinate plane. You may arrange the functions in any order you choose, but label each section of the graph with the corresponding function for your instructor to view.

Answer 7

thats all of the questions im on the first part of question b

Answer 8

ii chose g(x)=x^3-x^2-4x+4

Answer 9

what happens when you plug x = 0 into f(x) = x^2+2x+8 ? What is the output?

Answer 10

it would be just 8?

Answer 11

im sorry thats probably not correct..

Answer 12

yes it is 8, so the y intercept is 8

the parabola will cross the y axis at (0,8)

Answer 13

to find the x-intercepts, or roots, you would replace f(x) with 0 and solve for x

f(x) = x^2+2x+8
0 = x^2+2x+8
x^2+2x+8 = 0

Use the quadratic formula

Answer 14

okay so what next?

Answer 15

quadratic formula
\[\Large x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\]

Answer 16

plug in a = 1, b = 2, c = 8

Answer 17

is that supposed to be +

Answer 18

what do you mean?

Answer 19

this symbol ?

\[\Large \pm\]

Answer 20

yes

Answer 21

im sorry

Answer 22

that means "plus or minus"

it represents two different operations

Answer 23

oh

Answer 24

in reality, the quadratic will have two roots
\[\Large x = \frac{-b+\sqrt{b^2-4ac}}{2a}\]
or
\[\Large x = \frac{-b-\sqrt{b^2-4ac}}{2a}\]

Answer 25

the only difference between those last two equations is the plus is a minus or vice versa. So most books will condense the two equations into one equation and use the "plus/minus" symbol

Answer 26

oh

Answer 27

okay so \[x=-b-\sqrt{?}b^2-4ac\]

Answer 28

that came out wrong

Answer 29

let's just focus on the b^2 - 4ac part for now

Answer 30

if a = 1, b = 2, and c = 8, then what is b^2 - 4ac equal to?