Answer:If a graph of a quadratic,
f
(
x
)
, does not have an x-intercept
then
f
(
x
)
=
0
has no Real solutions.
Step-by-step explanation:
The x-axis is composed of all points for which
f
(
x
)
(or, if you prefer,
y
) is equal to
0
If the graph of
f
(
x
)
does not have an x-intercept
then it has no (Real) points for which
f
(
x
)
=
0
Step-by-step explanation:
No x-intercept means that it does not cross the x-axis. Thus two solutions is definitely ruled out.
However, if you DO NOT INCLUDE a point of coincidence (Vertex coincides with the x-axis) in the phrase "does not have an x-intercept". Then there could be a single value solution if you equate the quadratic to 0. Some people say that it still has two in such a case but they are both the same value. I do not like this way of thinking!
On the other hand, if you DO INCLUDE a point of coincidence in the phrase, then the plot does not cross the x-axis nor does any point on the curve coincide with it. In such an interpretation there is NO SOLUTION THAT IS REAL. hopes this helps