Question

the equation of the flight path of an object is given by the equation h=4+2x-x^2.
A) calculate the maximum height of an object?

Answer 1

To find the maximum height of the object described by the equation \( h = 4 + 2x - x^2 \), we can use the method of completing the square or we can find the vertex of the parabola since this is a quadratic equation of the form \( h(x) = ax^2 + bx + c \).

Here, we can identify:
- \( a = -1 \)
- \( b = 2 \)
- \( c = 4 \)

The maximum height occurs at the vertex of the parabola, and the x-coordinate of the vertex can be found using the formula:

\[
x = -\frac{b}{2a}
\]

Substituting the values of \( a \) and \( b \):

\[
x = -\frac{2}{2(-1)} = -\frac{2}{-2} = 1
\]

Now, we can substitute \( x = 1 \) back into the equation to find the maximum height \( h \):

\[
h = 4 + 2(1) - (1)^2
\]
\[
h = 4 + 2 - 1
\]
\[
h = 5
\]

Thus, the maximum height of the object is \( \boxed{5} \).