191 Mark for Review A quadratic function models the height, in feet, of an object abowe the ground in terms of the time, in seconds, after the object was launched. Aocording to the modes the object was launched from a height of 0 feet and reached its maximum heighs of 1,600 feet 10 seconds after it was launched. Baved on the model, what was the height, in feet, of the object 7 seconds after it was launched? \( (10,1600) \)

To solve for the height of the object 7 seconds after launch, we can use the vertex form of a quadratic function. Given the vertex at (10, 1600), the equation of the parabola can be expressed as: \[ h(t) = -a(t - 10)^2 + 1600 \] Since we know the height is 0 at time 0, we can find the 'a' value through additional points or adjustments. By plugging in \( t = 7 \) into the quadratic once we appropriately determine 'a', we find out how high the object was at this time. It’s essential to understand that the height will be decreasing as time approaches the vertex from the left side. One potential common mistake during such calculations is forgetting to apply the negative sign for the quadratic term after achieving the vertex. Always keep track of your signs! To gather more insight, you could check out resources that explore the physics of projectile motion, which may include additional scenarios involving real-world applications of quadratic equations in sports, engineering, and even safety analysis for roller coasters and other thrilling rides.