 # Create and Graph Quadratic Equations

Related Topics:
Algebra Word Problems
Common Core (Algebra)
Common Core for Mathematics

Examples, solutions, videos, and lessons to help High School students learn how to create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

### Suggested Learning Targets

• Create equations in two or more variables to represent relationships between quantities.
• Graph equations in two variables on a coordinate plane and label the axes and scales.
Common Core: HSA-CED.A.2

Application of Quadratic Equations - Modeling and Graphs
This video looks at an example of a quadratic equation modeling the height of diver t seconds after he dives off a platform. We find the time it takes to reach various heights and we find the maximum height.

A frog jump to catch a grasshopper. The frog reaches a maximum height of 25cm and travels a horizontal distance of 100cm. A grasshopper, located 30cm in front of the frog, starts to jump at the same time as the frog. The grasshopper reaches a maximum height of 36cm and travels a horizontal distance of 48cm. The frog and the grasshopper both jump in the same direction.

a) Consider the frog's starting position to be at the origin of a coordinate grid. Draw a diagram to model the given information.
b) Determine a quadratic equation to model the frog's height and the grasshopper's height as a function of the horizontal distance travelled.
c) Solve the system of equation and interpret your solution in the context of this problem.

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