Question

Now that the curve pieces are decided, 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. first coaster g(x) = (x + 2) (x − 1) (x − 2)

second coaster f(x) =(x-1) (x -2)

Answer 1

The process of obtaining the equation is similar, but it is more algebraically intensive. Given the focus (h,k) and the directrix y=mx+b, the equation for a parabola is (y - mx - b)^2 / (m^2 +1) = (x - h)^2 + (y - k)^2.

1) Standard form: y = ax2 + bx + c where the a,b, and c are just numbers.

2) Factored form: y = (ax + c)(bx + d) again the a,b,c, and d are just numbers.

3) Vertex form: y = a(x + b)2 + c again the a, b, and c are just numbers.

These three main forms that we graph parabolas from are called standard form, intercept form and vertex form. Each form will give you slightly different information and have its own unique advantages and disadvantages.

Explanation: