|Direction||Vertex||Axis of Symmetry||y-intercept|
Now, find all the points on the graph that have a y-coordinate equal to 0.
The x-coordinates of the identified points solve the equation f(x)=0.
seeits factors. Consider the following expression.
It is known that a=4 and c=3, so ac=12>0. Therefore, the factors must have the same sign. Also, b=13. Since the sum of the factors is positive and they must have the same sign, both factors must be positive. All positive factor pairs of 12 can now be listed and their sums checked.
|Factors of ac||Sum of Factors|
|1 and 12|
|2 and 6|
|3 and 4|
In this case, the correct factor pair is 1 and 12. The following table sums up how to determine the signs of the factors based on the values of ac and b.
|Negative||Positive||One positive and one negative. The absolute value of the positive factor is greater.|
|Negative||Negative||One positive and one negative. The absolute value of the negative factor is greater.|
Such analysis makes the list of possible factor pairs shorter.