Question 9 (10 points) If a toy rocket is launched vertically upward from ground level with an initial velocity of 128 feet per second, then its height h, after t seconds is given by the equation h(t)=-16t^2+128t (air resistance is neglected) How long did it take the toy rocket to reach its maximum height? 6 seconds b 4 seconds 2 seconds d 1 second

## Step 1<br />The given equation is a quadratic equation in the form of \( ax^2 + bx + c \), where \( a = -16 \), \( b = 128 \), and \( c = 0 \). The maximum height of the toy rocket is reached at the vertex of the parabola represented by this equation.<br /><br />## Step 2<br />The x-coordinate of the vertex of a parabola given by the equation \( ax^2 + bx + c \) is given by the formula \( -b/2a \).<br /><br />### **The formula for the x-coordinate of the vertex is \( -b/2a \)**<br /><br />## Step 3<br />Substitute the values of \( a \) and \( b \) into the formula to find the time \( t \) when the maximum height is reached.<br /><br />### **Substitute \( a = -16 \) and \( b = 128 \) into the formula to get \( t = -128/(2*-16) \)**