Digital SATMath: AlgebraMedium
A scientist is tracking the trajectory of a launched probe. The height of the probe, h(t), in meters above the ground, after t seconds, is given by the equation h(t) = -4.9t^2 + 98t + 10. At what time does the probe reach its maximum height?
- A20 seconds
- B10 seconds
- C5 seconds
- D15 seconds
Show answer & explanationAnswer & explanation
Correct answer: B. 10 seconds
The equation is a quadratic function in the form at^2 + bt + c. The time at which the maximum height is reached is given by the vertex formula t = -b / (2a). Here, a = -4.9 and b = 98. So, t = -98 / (2 * -4.9) = -98 / -9.8 = 10 seconds.
Why the other options are wrong
- A. Incorrect calculation; potentially found the time when it returns to a certain height, not the maximum.
- C. Incorrect calculation; possibly a division error or misidentification of 'a' and 'b'.
- D. Incorrect calculation; does not correspond to the vertex formula.
Vertex of a Parabola (Quadratic Function)
The highest or lowest point on the graph of a quadratic function, representing the maximum or minimum value of the function.
- For h(t) = at^2 + bt + c, the x-coordinate (or t-coordinate) of the vertex is given by -b/(2a).
- If 'a' is negative, the parabola opens downward, and the vertex is a maximum.
- If 'a' is positive, the parabola opens upward, and the vertex is a minimum.
Memory trick: Vertex is 'Very' important, use '-b over 2a' to find it.