SOLUTION: Can you please help me to sketch the graph, given is y=ax^2+bx+c where a<0 ; b<0 ; c<0 and ax^2+bx+c has only one solution.

Question 1078174: Can you please help me to sketch the graph, given is y=ax^2+bx+c where a<0 ; b<0 ; c<0 and ax^2+bx+c has only one solution.
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
You mean that has only one solution.

If a<0 the graph opens down (like a frowny mouth),
and goes down without a bottom on the left end and on the right end,
like
, or , or .
That means there are at least some points below the x-axis.
In this specific case, because b<0 and c<0 too,
it is also obvious that for .
If there were also some points above the x-axis
the graph would have to cross the x-axis twice,
but the fact that has only one solution
means that it just touches it once and does not cross it,
like , or , or .

I do not know if it was your teachers intention,
but the point where the graph touches the x- axis
must have .
Did you learn in class that the vertex of the graph
is at ?
If both (a and b) are negative,
that is ,
so the graph can look like , or ,
touching the x-axis to the left of the origin.
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