## Reflection: Developing a Conceptual Understanding How long will it take? (Day 1 of 2) - Section 2: New Information

It was not clear to some of the learners why the quadratic 2x= 32 was "separated" into two equations y = 2xand y = 32, when graphing to find the solutions. Some did not understand why a line?...why a parabola?  and why the intercepting points are the solutions? These were some of the questions that I can remember.

First, it may be a good idea to remind students that the points on a line or curve are the solutions to the equation of that line or curve. Take the two linear equations y = x + 5   and  y = 2x and graph both on the same plane so that the learners  see that they both intersect at the point with coordinates (5, 10). This is the only point that is a solution to both equations....the intersecting point. Ask them to substitute 5 into both equations to verify this. When x is 5, y is 10 in both equations.

I would then ask them if the following is true.... x + 5 = 2x

Students will see that this is true by substitution. (You may want to refer to the transitive property as well) Ask students to solve for x and they will get 5 as the answer.

In reference to our quadratic  2x2 = 32, the line y = 32 intersects the parabola in two places, where the abscissa is -4 and where it is 4. The ordinate is 32 at both of these and solving for x in the equation gives us +4 and - 4.

Student Thinking about Graphical Solutions using a Systems Approach
Developing a Conceptual Understanding: Student Thinking about Graphical Solutions using a Systems Approach

# How long will it take? (Day 1 of 2)

Unit 8: Advanced Equations and Functions
Lesson 5 of 7

## Big Idea: How long will it take an object to hit the ground if it falls from the top of Chicago’s John Hancock Center which is 1,127 ft. high? This lesson will help us solve equations to answer questions like this one!

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50 minutes

### Mauricio Beltre

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