You can put this solution on YOUR website! if it doesn't look like it can be factored, or if it doesn't look like it can be factored easily, then you use the quadratic formula.
the equation you are trying to solve is y = 4x^2 + 24x + 35
to factor it, set y equal to 0 and you get:
4x^2 + 44x + 35 = 0
that equation is now in standard quadratic form of ax^2 + bx + c = 0
in your equation:
a = 4
b = 24
c = 35
the quadratic formula is x = (-b +/- sqrt(b^2 - 4ac)) / 2a.
when you solve using the quadratic formula, you get x = -28/8 and x = -20/8.
those are not integers so the assumption that the formula couldn't be factored is correct.
confirm your answers are correct by substituting in the original equation.
when x = -8/28, 4x^2 + 24x + 35 is equal to 0, so that solution is good.
when x = -20/8, 4x^2 + 24x + 35 is equal to 0, so that solution is good.
the graph of your equation is shown below:
-28/8 is equal to -3.5
-20/8 is equal to -2.5
you can see that the graph of the equation of y = 4x^2 + 24x + 35 crosses the x-axis at those points.
those are called the roots of the equation or the zeroes of the equation which is when y is equal to 0.
