a firework is modelled by the relation h=-4.9(t-9)^2+170 h=height above ground in metres and t=time in seconds
what are the co-ordinates of the vertex of this parabola?
h = (t-9)^2 + 170
h is least when t = 9s
The value of h there is 170.
The vertex is therefore at
t = 9; h=170
your equation
h=-4.9(t-9)^2+170
is in the standard form of the "vertex" form of a quadratic function,
the vertex is (9, 170)
[standard form ...
if y = a(x-h)^2 + k , the vertex is (h,k) ]
To find the coordinates of the vertex of the parabola represented by the relation h = -4.9(t - 9)^2 + 170, we can compare it to the standard form of a quadratic equation: y = a(x - h)^2 + k.
In this case, h represents the horizontal shift, and k represents the vertical shift of the vertex. The coordinates of the vertex are (h, k).
Comparing the given equation to the standard form, we can see that a = -4.9, h = 9, and k = 170.
Therefore, the coordinates of the vertex of this parabola are (9, 170).
To find the coordinates of the vertex of a parabola in the form y = ax^2 + bx + c, you can use the formula:
x = -b / (2a)
In the given relation h = -4.9(t-9)^2 + 170, we can rewrite it as:
h = -4.9t^2 + 88.2t + 43.21
Now we can identify the values of a, b, and c. In this case, a = -4.9, b = 88.2, and c = 43.21.
Using the formula for the x-coordinate of the vertex, we can substitute these values:
x = -88.2 / (2 * -4.9)
Simplifying this equation, we get:
x = -88.2 / -9.8
x = 9
Now, to find the y-coordinate of the vertex, we substitute this value back into the original equation:
h = -4.9(9-9)^2 + 170
Since (9-9)^2 is equal to 0, this eliminates the term involving t. Thus, we are left with:
h = 170
Therefore, the coordinates of the vertex of the parabola are (9, 170).