You can put this solution on YOUR website! the roots are at x = -1/4 and x = 3.
set these equations to 0 by doing the following.
add 1/4 to both sides of x = -1/4 to get x + 1/4 = 0
subtract 3 from both sides of x = 3 to get x - 3 = 0
the factors of the quadratic equation are (x + 1/4) * (x - 3) = 0
set the equation equal to y and simplify to get:
y = x^2 - 3x + 1/4 * x - 3/4
combine like terms to get y = x^2 - 2.75x - 3/4
in fact, the quadratic equation can be a * (x^2 - 2.75x - 3/4)
if a = 1, you get x^2 - 2.75x - 3/4.
if a = 4, you get 4x^2 - 11x - 3.
a can be any value and the roots of the equation will be the same.
the graph above shows the basic equation of x^2 - 2.75x - 3/4 with various values of a to show that the roots remain the same even though the quadratic equation itself is different after being gernerated by the diffedrent values of a.
the two versions of the red equation show you that they are, in fact, the same equivalent equations that generate the same red graph.
here's the graph.
