Please show full work.

1. Two people stood 3m apart and 1.5 m vertically above the ground. Person A threw a ball to Person B (path was a parabola in form y = ax + bx + c, where x is the horizontal distance the ball travelled and y is the height above the ground). When the horizontal distance was 1 (x=1) the slope of the tangent was 1 (y'=1). Determine the maximum height of the ball using calculus methods only. All work must be shown. y = ax + b x+ c 15 m 3 m