Question

For number 7 I need an explanation with steps for why is true or false
Thank you

Answer 1

Part 1) The statement is false

Part 2) The statement is false

Part 3) The statement is true

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

`h(t)=-16t^(2) +72t`

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

`h(t)=-16t(t-4.5)`

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

`0=-16t(t-4.5)`

so

`(t-4.5)=0`

`t=4.5\ sec`

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

`h(t)=-16t^(2) +72t`

`h(t)=-16(t^(2) -4.5t)`

`h(t)-81=-16(t^(2) -4.5t+2.25^(2))`

`h(t)-81=-16(t-2.25)^(2)`

`h(t)=-16(t-2.25)^(2)+81` ---> quadratic equation in vertex form

The vertex is a maximum

The vertex is the point (2.25,81)