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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.
2.) 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.
3.) Create a graph of the polynomial function you created in Question 4.
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This is the first part:
Ray and Kelsey have summer internships at an engineering firm. As part of their internship, they get to assist in the planning of a brand new roller coaster. For this assignment, you help Ray and Kelsey as they tackle the math behind some simple curves in the coaster's track.
The first part of Ray and Kelsey's roller coaster is a curved pattern that can be represented by a polynomial function.
1.) 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.
Yes, Ray and Kelsey could both be correct. They could have a third degree polynomial that crosses the x-axis 3 times but the y-axis only 1 time, which would make both Ray and Kelsey right.
2.) 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
The key features of g(x) = x3 − x2 − 4x + 4 include:
The Function Is Equal To: 0
Zeros Of This Function Are: -2, 2, and 1
End Behavior: Falls to the left and goes up to the right.