Create and Graph Quadratic Equations

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.

Writing Quadratic Models Graphs

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Graphing Quadratic Functions

Quadratic Equations
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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