Answer:
The vertex is at the point (50,103). The arrow will reach the highest point 50 feet horizontal distance and 103 feet vertical distance from where it was launched.
Step-by-step explanation:
The equation of a parabola is given by:
[tex]y=ax^2+bx+c[/tex]
The vertex is the maximum or minimum value of the parabola
In this case, we have the following parabola:
[tex]y=-0.04 x^2+4x + 3[/tex]
where
a=-0.04
b=4
c=3
The x-coordinate of the vertex can be found by the formula:
[tex]x=\frac{-b}{2a}[/tex]
Then, we find the x-coordinate by replacing the values of a nd b:
[tex] x=\frac{-b}{2a} \\ x=\frac{-(4)}{2\times (-0.04)} \\ x=50[/tex]
Next, we replace the value of x in the parabola equation:
[tex]y=-0.04 x^2+4x + 3 \\ y =-0.04\times 50^2+4\times 50 + 3 \\ y =-100+200+ 3 \\ y=103[/tex]
The vertex is at the point (50,103)
