Fill in the Blank 3 points A football is punted into the air. It's height, I, In feet,aftert seconds is given by the equation h(t)=-4.9t^2+20.5t+1 a) What is the x-value of the vertex?Round to the nearest tenth. square b) What does the x-value of the vertex represent in the context of this problem? That number is the maximum height. That's when the ball hits the ground. #At that time (in seconds)the football reaches its max height.

To solve this problem, we need to find the vertex of the quadratic equation \( h(t) = -4.9t^2 + 20.5t + 1 \). The vertex form of a quadratic equation \( ax^2 + bx + c \) can be found using the formula for the x-coordinate of the vertex:<br /><br />\[ t = -\frac{b}{2a} \]<br /><br />Here, \( a = -4.9 \), \( b = 20.5 \), and \( c = 1 \).<br /><br />a) Calculate the \( x \)-value (or \( t \)-value in this context) of the vertex:<br /><br />\[ t = -\frac{20.5}{2(-4.9)} \]<br />\[ t = -\frac{20.5}{-9.8} \]<br />\[ t = \frac{20.5}{9.8} \]<br />\[ t \approx 2.1 \]<br /><br />So, the \( x \)-value of the vertex is approximately 2.1 seconds.<br /><br />b) In the context of this problem, the \( x \)-value of the vertex represents the time at which the football reaches its maximum height. <br /><br />Therefore, the completed statements are:<br /><br />That number is the maximum height.<br />: That's when the ball hits the ground.<br />At that time (in seconds), the football reaches its max height.