Thread: Precalc chapter project finding points of intersection

Hi! I am a student teacher and have the following project worked out:

In this project the student will find the points of intersection of the circle and parabola given by
x^2 +y^2-3x + 5y -11 and y = x^2 -4x + 5

a. Begin by writing the circle as the union of two functions. Identify the functions that represent the top half and the bottom half of the circle.

top half y = .5(-5 + sqrt(69 + 12x -4x^2)
bottom half y = .5(-5 - sqrt(69 + 12x -4x^2)

b. Use a graphing utility to graph all thre functions in the same viewing window. Use the intersect feature of the graphing utility to estimate the points of intersection.
(1.055, 1.893), (2.841, 1.707)

There are also four more questions they have to answer. My question is this, My coorporating teacher gives the students a hint to get them on thier way and I don't want to give them too much. This is a chapter project for an honors class and would appreciate any ideas for a subltle hint for the students. I told one student to look on page 8 of the text which had examples of problems dealing with equations of circles. Do you think this enough of a hint or should I give them a little more?

Thank You for taking time to read this. I just want to get them in the right direction without giving them too much and making it easy for them.

Thank You,
Keith

Which class is this?

If it's post-algebra2, won't they just substitute the equation of the parabola into the equation of the circle, then solve for x? This seems like a 10 minute ordeal at best for an honors class.

Idea: Perhaps they need to find the above intersection in a set of intersection problems. circle with linear, circle with quadratic, circle with other circle, etc.

Useful idea:
- Given the any two of the above objects, what is the fewest|exact|largest number of intersections? Sketch examples of each case.