standard_description: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.
problem_activity: Task
The first three steps of three visual patterns are shown below.
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Here are functions that define how many tiles are in step $n$, in no particular order: $$f(n)=3n^2$$ $$g(n)=n^2+4$$ $$h(n)=n^2-1$$
Decide which function defines which pattern.
One of these patterns has a step with $432$ tiles in it, one has a step with $195$ tiles in it, and one of these patterns has a step with $404$ tiles in it. Decide which is which, find the step that contains that number of tiles, and explain how you know.
Describe and justify the steps to solve this equation for $x$. $$ax^2+c=d$$


aligns: no