An advantage of the factored form of a quadratic function is that you can determine the x-intercepts of its graph very easily. Recall that x-intercepts occur when the entire function (y-value) is equal to zero. This happens when either factor is equal to zero.

So, for the factored form of the function , if x = 3 or x = 4, the entire function would have a value of zero.

As such, the graph of the function will have x-intercepts at x = 3 and x = 4.

Because these x-values make the function equal to 0, they are also referred to as the zeros of the function.

In standard form, you can tell the direction of opening of the parabola by inspecting the a-value of the function. Since it is convention to factor out a negative coefficient on the x2 term of a trinomial before factoring by decomposition, the sign of the greatest common factor will tell you the direction of opening of the parabola when the function is given in factored form.

So, for the factored form of the function , since the GCF is positive 2, the graph of the function will open up.

Other parts of the graph can be interpreted like you did with standard form. The following table summarizes information from the factored form of a quadratic equation.

Interpreting the factored form of a quadratic function
zeros/x-intercepts can be determined by setting each factor equal to zero and then solving for x
direction of opening up when the GCF of a is positive and down when the GCF of a is negative. If there is no identified GCF, then the GCF is positive 1 and the graph will open up.
y-intercept let x = 0 and determine the value of y
axis of symmetry half-way between the x-intercepts of the graph (or roots of the function)—an easy task since the x-intercepts can easily be determined from this form
vertex enter the x-value of the axis of symmetry into the equation of the function to determine the y-value