Answer:
Part 1) The statement is false
Part 2) The statement is false
Part 3) The statement is true
Step-by-step explanation:
Let
h(t)-----> the height of an object launched to the air
t ----> the time in seconds after the object is launched
we have
[tex]h(t)=-16t^{2} +72t[/tex]
Verify each statement
case 1) The factored form of the equation is h(t)=-16(t-4.5)
The statement is false
Because
The factored form is equal to
[tex]h(t)=-16t(t-4.5)[/tex]
case 2) The object will hit the ground at t=72 seconds
The statement is false
Because
we know that
The object will hit the ground when h(t)=0
substitute in the equation and solve for t
[tex]0=-16t(t-4.5)[/tex]
so
[tex](t-4.5)=0[/tex]
[tex]t=4.5\ sec[/tex]
case 3) The t-value for the maximum of the function is 2.25
The statement is true
Because
Convert the quadratic equation in vertex form
[tex]h(t)=-16t^{2} +72t[/tex]
[tex]h(t)=-16(t^{2} -4.5t)[/tex]
[tex]h(t)-81=-16(t^{2} -4.5t+2.25^{2})[/tex]
[tex]h(t)-81=-16(t-2.25)^{2}[/tex]
[tex]h(t)=-16(t-2.25)^{2}+81[/tex] ---> quadratic equation in vertex form
The vertex is a maximum
The vertex is the point (2.25,81)
