Level 1- 1 problem 1) Aylin is a professio nal softball player.The height (yards) of the softball after she hits it is given by the equation h(t)=48t-16t^2 , where t represents the time in seconds after the hit . What is the maximum height the softball reaches? 2

To find the maximum height the softball reaches, we need to determine the vertex of the parabola represented by the equation $h(t) = 48t - 16t^2$. The vertex of a parabola in the form $y = ax^2 + bx + c$ is given by the formula $x = -\frac{b}{2a}$.<br /><br />In this case, the equation is in the form $h(t) = -16t^2 + 48t$, so $a = -16$ and $b = 48$.<br /><br />Using the formula for the vertex, we have:<br />$x = -\frac{b}{2a} = -\frac{48}{2(-16)} = \frac{48}{32} = 1.5$<br /><br />Now, we can substitute $t = 1.5$ back into the original equation to find the maximum height:<br />$h(1.5) = 48(1.5) - 16(1.5)^2 = 72 - 36 = 36$<br /><br />Therefore, the maximum height the softball reaches is 36 yards.