If we know the roots (solutions) we can find the equation of the second-degree function using the formula above:
[tex]f(x)=a(x-x_1)(x-x_2)[/tex]
In this case, a = -1, x1 = 2 and x2 = 4. Therefore the equation will be:
[tex]f(x)=-1(x-2_{})(x-4_{})[/tex][tex]f(x)=-x^2+6x-8[/tex]
The vertex is maximum (see that the function has a clear max value).
The solutions to the function are the roots (place in the x-axis where the function cross). They are 2 and 4.
The y-intercept is the point with the format (0,y). Thus to find this point we can substitute 0 into the function:
[tex]f(0)=-0^2+6\times0-8[/tex][tex]f(0)=-8[/tex]
The y-intercept will be y = -8.
