A football is kicked into the air. Its height in meters after t seconds is given by h=-5(t-2)^2+20
What was the height of the football when it was kicked?
Is it right the y intercept is 0,0 and x intercept is (0,0) and (4,0)?
yes, when t = 0, h = -20+20 = 0
if you are graphing (t,h) yes
when t = 0, h = 0 (0,0)
h = 0 when t is 0 and 4 (0,0) and (4,0)
To find the height of the football when it was kicked, we need to determine the value of h when t is equal to 0.
Given the equation representing the height of the football is h = -5(t-2)^2 + 20, we substitute t = 0 into the equation:
h = -5(0-2)^2 + 20
h = -5(-2)^2 + 20
h = -5(4) + 20
h = -20 + 20
h = 0
Therefore, the height of the football when it was kicked is 0 meters.
Regarding the x-intercepts, x-intercepts occur when the value of y is equal to zero. To determine the x-intercepts, we set the equation equal to zero and solve for t:
-5(t-2)^2 + 20 = 0
To solve this quadratic equation, we can factor it:
-5(t-2)(t-2) + 20 = 0
Simplifying further:
-5(t-2)^2 + 20 = 0
Next, we subtract 20 from both sides of the equation:
-5(t-2)^2 = -20
Divide both sides by -5:
(t-2)^2 = 4
To find the solutions, we take the square root of both sides:
t - 2 = ±2
Solving for t:
t = 2 ± 2
This gives us two possible values for t: t = 0 and t = 4.
Therefore, the x-intercepts are (0,0) and (4,0).