Answer:
4 meters
Step-by-step explanation:
Given a quadratic equation in which the coefficient of [tex]x^2[/tex] is negative, the parabola opens up and has a maximum point. This maximum point occurs at the line of symmetry.
Since the divers height, y is modeled by the equation
[tex]y= -x^2 + 2x + 3[/tex]
Step 1: Determine the equation of symmetry
In the equation above, a=-1, b=2, c=3
Equation of symmetry, [tex]x=-\dfrac{b}{2a}[/tex]
[tex]x=-\dfrac{2}{2*-1}\\x=1[/tex]
Step 2: Find the value of y at the point of symmetry
That is, we substitute x obtained above into the y and solve.
[tex]y(1)= -1^2 + 2(1) + 3=-1+2+3=4m[/tex]
The maximum height of the diver is therefore 4 meters.
