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Course: Integrated math 3 > Unit 7

Lesson 5: Quadratic systems
Math
Integrated math 3
Equations
Quadratic systems
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Quadratic systems

Google Classroom

Problem

The circle given by (x−1)2+(y−1)2=1 and the line given by y=2x+1 are graphed.
Two graphs on an x y coordinate plane. The x- and y- axes scale by one. The first graph is a line slanting upwards from left to right through the points, (zero, one) and (one, three). The second graph is a circle where the center is at (one, one). It has a radius of one and passes through the points (one, zero), (two, one), (one, two), and (zero, one).
We want to find their intersection points.
1) One intersection point is clearly identifiable from the graph. What is it?
(
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
,
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
)
2) Find the other intersection point.
Your answer must be exact.
(
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
,
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
)