Interpret key graph/table features of quadratic models in context.
Interpret the y-intercept of a quadratic model in context
Problem
Find and interpret the \(y\text{-}\text{intercept}\) of \(h(t)=-16t^{2}+48t+5\), where \(t\) is seconds and \(h\) is feet. Evaluate \(h(0)\), give the intercept point, and state what the output means at launch.
Big Picture
What this problem is really about
A vertical intercept is the output produced when the model’s input is zero, which often represents an initial condition. We’ll substitute zero into the complete rule, preserve the result as an ordered point with units, and identify what the zero-input instant means in this situation.
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