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 can be found using the formula for the x-coordinate of the vertex: Here, , , and .a) Calculate the -value (or -value in this context) of the vertex: So, the -value of the vertex is approximately 2.1 seconds.b) In the context of this problem, the -value of the vertex represents the time at which the football reaches its maximum height. Therefore, the completed statements are: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.