Question

After a dreary day of rain, the sun peeks through the clouds and a rainbow forms. You notice the rainbow is the shape of a parabola. The equation for this parabola is y = -x2 + 36. Create a table of values for a linear function. A drone is in the distance, flying upward in a straight line. It intersects the rainbow at two points. Choose the points where your drone intersects the parabola and create a table of at least four values for the function. Remember to include the two points of intersection in your table. Analyze the two functions. Answer the following reflection questions in complete sentences. What is the domain and range of the rainbow? Explain what the domain and range represent. Do all of the values make sense in this situation? Why or why not? What are the x- and y-intercepts of the rainbow? Explain what each intercept represents. Is the linear function you created positive or negative? Explain. What are the solutions or solution to the system of equations created? Explain what it or they represent.

Answer 1

Okay assuming that this is y=-x^2+36.

Vertex form: y=-x^2+36
Intercept form: y=(-x-6)(x-6)
Vertex: (0,36)
Focus: (0,143/4)=(0,35.75)
Directrix: y=145/4=36.25
Axis of Symmetry: x=0
Focal parameter (distance between the directrix and focus): 1/2=0.5
x-intercepts: (-6,0), (6,0)
y-intercepts: (0,36)

I hope this helps.