SAT Math Multiple Choice Question 273: Answer and Explanation
A physics class is using simulation software to study water bottle rockets before attempting to build one for the National Physics Competition. Their first simulation is of a rocket without a parachute launched from the roof of the gymnasium. The scatterplot shows the approximate path of the rocket. The software program generates the equation h = –4.9t2 + 39.2t + 14 to model the data, where h is the height in meters of the rocket t seconds after it was launched. What does the number 14 most likely represent in this equation?
- A. The number of seconds the rocket was in the air
- B. The height of the gymnasium from which the rocket was launched
- C. The number of seconds that it took the rocket to reach its maximum height
- D. The maximum height of the rocket
Correct Answer: B
Category: Passport to Advanced Math / Quadratics
Strategic Advice: When a quadratic equation is written in standard form, y = ax2 + bx + c, the value of c is the y-intercept of the equation's graph. This is because substituting 0 for x results in y = a(0)2 + b(0) + c = c.
Getting to the Answer: In a real-world scenario, the y-intercept represents an initial amount. In this question, height is what is being measured, so the y-intercept represents the initial height of the bottle rocket. Because the rocket was fired from the roof of the gymnasium, the height of the gymnasium must be 14 meters, making (B) correct.