Question 1
Where does the following equation intercept the x-axis?
and
and
and
and
only
Explanation: To determine where an equation intercepts a given axis, input 0 for either 
(where it intercepts the 
-axis) or 
(where it intercepts the 
-axis), then solve. In this case, we want to know where the equation intercepts the 
-axis; so we will plug in 0 for 
, giving:
Now solve for 
.
Note that in its present form, this is a quadratic equation. In this scenario, we must find two factors of 12, that when added together, equal 7. Quickly, we see that 4 and 3 fit these conditions, giving:
Solving for 
, we see that there are two solutions,
or 
(where it intercepts the -axis) or (where it intercepts the -axis), then solve. In this case, we want to know where the equation intercepts the -axis; so we will plug in 0 for , giving:
Now solve for .
Note that in its present form, this is a quadratic equation. In this scenario, we must find two factors of 12, that when added together, equal 7. Quickly, we see that 4 and 3 fit these conditions, giving:
Solving for , we see that there are two solutions,
or