document.write( "Question 831047: Azim is the best basketball playerof all time.The height of his basketball shot from the top of his head is modeled by the function h(t)=-t^2+4t+6, h(t) us vertical displacement from his head and t is is time in seconds. Azim is 6 feet tall and standing on the ground. What is the maximum height in feet that the ball will reach from the ground? \n" ); document.write( "

Algebra.Com's Answer #501104 by brysca(112) $\"\"$ $\"About$

You can put this solution on YOUR website!
If the graph is drawn out, it shows the trajectory of the basketball if it were to be shot by Azim.\r
\n" ); document.write( "\n" ); document.write( "The goal is to find the y value of the vertex in the equation, which will be the maximum height that the ball reaches.\r
\n" ); document.write( "\n" ); document.write( " Remember that the $\"-%28t%5E2%29\"$ part in the function is negative so the parabola is pointing downwards. Negative parabolas have maximums which is the vertex.\r
\n" ); document.write( "\n" ); document.write( "The expression for the vertex of a parabola is $\"x+=+%28-b%29%2F%282%2Aa%29+\"$ .
\n" ); document.write( "So if you plug in the numbers corresponding to the equation it should look like this\r
\n" ); document.write( "\n" ); document.write( " $\"%28-%284%29%29%2F%282%2A-1%29+\"$ This should give you an answer of 2. Now, the expression for vertex is an equation for the x value of the vertex.
\n" ); document.write( "So, you need to find the y value. You do this by plugging 2 into the equation
\n" ); document.write( " $\"h%28t%29=-t%5E2%2B4t%2B6%2C+h%28t%29\"$ which would look like this
\n" ); document.write( " $\"-%282%29%5E2%2B%284%2A2%29%2B6\"$ \r
\n" ); document.write( "\n" ); document.write( "Which gives you a y value of 10. The basketball will reach a maximum height of 10 feet. \n" ); document.write( "

\n" );