Journal 10 A projectile is launched from a height of \( 10^{\prime} \) and follows a path described by the formula \( h=-.2 x^{2}+135 x+10 \) where \( x \) is the distance the projectile has travelled downrange and \( h \) is the heig of the projectile. 1. Describe in your own words what the shape of path this would look like?(A)

The path described by the formula \( h = -0.2x^2 + 135x + 10 \) is a quadratic function, which means it will produce a parabolic shape. 1. **Shape of the Path:** - The coefficient of \( x^2 \) is negative (-0.2), indicating that the parabola opens downwards. This means that the projectile will rise to a certain height and then fall back down. - The term \( 135x \) suggests that the projectile has a significant initial upward velocity, causing it to rise quickly at first. - The constant term \( 10 \) indicates that the projectile starts at a height of 10 units (feet in this case). - As \( x \) (the distance traveled downrange) increases, the height \( h \) will initially increase, reach a maximum point (the vertex of the parabola), and then decrease as the projectile moves further downrange. In summary, the path of the projectile will resemble an upside-down "U" shape, starting at a height of 10 feet, rising to a peak, and then descending back towards the ground as it travels horizontally.