All courses Math II · A-SSE.1.a 8 of 73

Interpret terms, factors, and coefficients in quadratic and exponential expressions.

Interpret the leading coefficient of a quadratic expression

Problem

h(t)=−16t²+48t+5 models height h in feet at time t seconds. Enter leading coefficient with units, sign/opening effect, quadratic scale or second derivative, contextual consequence, and a guard against interpreting it as an ordinary constant slope.

Your answer

A leading coefficient=-16 feet/second²; sign effect=parabola opens upward; curvature=h''=32 feet/second²; consequence=height has a minimum B leading coefficient=-16 feet/second²; sign effect=opens downward; acceleration=-16 feet/second²; consequence=height has a maximum C leading coefficient=-16 feet/second²; sign effect=parabola opens downward; curvature=h''(t)=-32 feet/second²; physical meaning=-16 is one-half the constant vertical acceleration, not the acceleration itself; consequence=height has a maximum D leading coefficient=-16 feet/second; rate meaning=height drops16 feet every second; graph consequence=constant downward slope

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Interpret the leading coefficient of a quadratic expression

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Hint

Solution walkthrough

Identify the leading coefficient

Interpret the negative sign

Connect it to the projectile context

State the interpretation

Another way

Common mistake