The following graph describes the height of a football, where the height is measured in meters (m) and time in seconds (s). the What are the values of the zeros or -intercepts? X1=0, x2 =40 and State the value of the vertex. = (20,32) when the ball 30 m it was 25 and the ball when it is 32 m it was 20 s find the State the equation of the axis of symmetry
The zero or -intercept values are x1=0 and x2=40, which means that the football was on the ground at time 0 and after 40 seconds.
The vertex is at (20,32), which means that the maximum height of the football was 32 meters and it reached that height at 20 seconds.
When the football was at a height of 30 meters, it took 25 seconds to reach that height. When it was at a height of 32 meters, it took 20 seconds to reach that height.
To find the equation of the axis of symmetry, we use the formula x = -b/2a, where a is the coefficient of the x^2 term and b is the coefficient of the x term in the quadratic equation representing the height of the football.
The vertex form of a quadratic equation is y = a(x-h)^2 + k, where (h,k) is the vertex. In this case, we know that the vertex is (20,32), so the equation is y = a(x-20)^2 + 32.
To find the value of a, we can use the fact that the ball touches the ground at x=0 and x=40, so we have two points: (0,0) and (40,0). Plugging these into the equation and solving for a, we get:
0 = a(0-20)^2 + 32 -> a = 0.04
Now we can find the axis of symmetry:
x = -b/2a = -0/2(0.04) = 0
So the equation of the axis of symmetry is x = 0, which means that the maximum height is reached at the halfway point (20 seconds) between the two zeros.