Using a quadratic function, we have that:
a) The rocket reaches a maximum height of 25 units.
b) The rocket reaches it's highest point after 2 seconds.
c) The rocket will be back on the ground after 7 seconds.
<h3>What is the equation of a parabola given it’s vertex?</h3>
The equation of a quadratic function, of vertex (h,k), is given by:
y = a(x - h)² + k
In which a is the leading coefficient.
For this problem, placing it in vertex form, the equation for the height h is given by:
h = -(x - 2)² + 25.
Hence the vertex is (2,25), which means that:
a) The rocket reaches a maximum height of 25 units.
b) The rocket reaches it's highest point after 2 seconds.
The rocket hits the ground when h = 0, hence:
-(x - 2)² + 25 = 0
(x - 2)² = 25
Applying the square root to both sides:
x - 2 = 5.
x = 7.
The rocket will be back on the ground after 7 seconds.
More can be learned about quadratic functions at brainly.com/question/24737967
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