At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
hELP! Part A 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.
@pooja195 please help
Here are my answers so far. 1. Yes, they could both be correct. Ray and Kelsey could have a third degree polynomial that crosses the x-axis three times and the y-axis only once. So, it would satisfy Ray and Kelsey’s arguments. 2.To find the zeroes of g (x)= x^3 – x^2- 4x + 4 set function equal to 0 and factor. Zeroes of this function is -2,2, and 1. Other key features include end behavior, y-intercept, and (when graphed) the axis of symmetry and the vertex. 3. https://www.desmos.com/calculator/c6cdfwkdd6 X-intercepts: -2, 2 and 1 Y-intercept: 4 End Behavior: falls to the left and goes up to the right 4. F(x) = 3x^2 + 9x +12 The ends are both going up in the parabola since the coefficient is positive. y-intercept: 12 5. To find the vertex, substitute the value of the axis of symmetry into the function for x. y= ax^2+bx+c will be an example. If the value of a (the coefficient) is positive, the vertex with be a min, but if the value of the is negative it will be max. 6. https://www.desmos.com/calculator/dtnra1ysky 7.
JUST NEED LAST PART!
I am confused on how to draw it. I know how to do the math.
please draw both graphs together, and consider the point at which they join each other
OKay give me 1 min./
Sorry here it is: https://www.desmos.com/calculator/auaei5v4gy
correct! We have two intersection points
so a possible choice can be this:
It wants me to. Here just read this part: 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.
Is that all i need?
yes! I think so!
Ok thank you! And are all of my answers good up there?
@Michele_Laino i don't get it when it says: but label each section of the graph with the corresponding function for your instructor to view.
yes! they are correct!
here is my drawing:
Thank you so much!