raven built a rocket for her science project and launched it from a platform to track its path. the hight in feet of the rocket above ground at time t seconds can be modeled by the equation h= -16t^2+32t+4 what is the maximum hight the rocket reaches

Answer:20ftStep-by-step explanation:-16t² + 32t + 4The main goal to find the maximum height is to find the vertex of the parabola because the vertex is always the minimum or the maximum value.To find the x value of the vertex, use the formula x = [tex]\frac{-b}{2a}[/tex]The a-value is the first coefficient and the b value is the second coefficient:x = [tex]\frac{-32}{-32}[/tex]x = 1We can say x = t because t is the x value in the equation.Now, we can substitute x back into the original equation to find the y-value for the vertex.y = -16t² + 32t + 4y = -16(1)² + 32(1) + 4y = -16(1) + 32 + 4y = -16 + 32 + 4y = 20In a word problem, height is typically the y-value and time is typically the x-value. Since t = x, the answer is 20.