SAT Math Multiple Choice Question 360: Answer and Explanation

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Question: 360

15. A projectile is any moving object that is thrown near the Earth's surface. The path of the projectile is called the trajectory and can be modeled by a quadratic equation, assuming the only force acting on the motion is gravity (no friction). If a projectile is launched from a platform 8 feet above the ground with an initial velocity of 64 feet per second, then its trajectory can be modeled by the equation h = –16t2 + 64t + 8, where h represents the height of the projectile t seconds after it was launched. Based on this model, what is the maximum height in feet that the projectile will reach?

  • A. 72
  • B. 80
  • C. 92
  • D. 108

Correct Answer: A

Explanation:

A

Difficulty: Hard

Category: Passport to Advanced Math / Quadratics

Strategic Advice: Quadratic equations can be written in several different forms, each of which reveals something special about the graph. The maximum value of a quadratic function is equal to the y-value of the vertex of its graph, so vertex form, y = a(x - h)2 + k, reveals the maximum.

Getting to the Answer: The quadratic equation is given in standard form, so use the method of completing the square to rewrite the equation in vertex form. Then, read the value of k to find the maximum height of the projectile.

The vertex is (2, 72), so the maximum height is 72 feet.

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