Amodel rocket is fired from the ground at time t=0, and it’s height is given in cm by the formula h=-490t^2 +1470t where t is measured in seconds.

write an equation to find when the height of the rocket is 980 cm.

solve the equation by factoring.

explain why there are two solutions to this problem.

Step-by-step explanation:

h = -490t² + 1470t

When h = 980:

980 = -490t² + 1470t

Simplifying:

0 = -490t² + 1470t - 980

0 = t² - 3t + 2

Factoring:

0 = (t - 1) (t - 2)

t = 1, 2

There are two solutions because the rocket first reaches the height of 980 cm as it's going up at 1 second, then it reaches that height again as it's coming down at 2 seconds.

the required function is .

step-by-step explanation:

from the given table it is noticed that the graph passing through (-3,7), (0,4), (3,1) and (8,-4).

it is a linear function because the value of y is decrease by one as the value of x increase by 1.

the slope of the function is

the slope of the function is -1 and the y-intercept is 4.

the slope intercept form is

where, m is slope and b is y-intercept.

therefore the required function is . the graph of this function is shown below.