An object is launched from a platform. Its height (in meters), \( x \) seconds after the launch, is modeled by \( h(x)=-5 x^{2}+20 x+60 \) What is the height of the object at the time of launch? meters

At the time of launch, \( x = 0 \) seconds. To find the height of the object at launch, substitute \( x \) in the equation \( h(x) \): \[ h(0) = -5(0)^2 + 20(0) + 60 = 60 \text{ meters} \] So, the height of the object at the time of launch is 60 meters. The quadratic equation represents a parabolic trajectory, which is common in projectile motion. The coefficients show that gravity pulls the object downward while an initial velocity gives it an upward move. Understanding this concept can help in predicting motion, whether it's for sports, engineering, or amusement park rides! If you’re diving into projectile motion problems, remember to look for the vertex of the parabola, which represents the maximum height. Often, the mistakes people make include forgetting to evaluate the function at the correct time or miscalculating the constants. Always double-check your math for those pesky negative signs and coefficient multipliers!