What is the sum of all numbers a for which the graph of y=x^2+a and the graph of y=ax intersect one time?
+2863 It intersects one time if they have ONE solution.
We substitute Y.
\(x^2+a=ax\)
Then we set it equal 0 so it matches the standard quadratic form.
\(x^2-ax+a=0\)
In order to find when it has ONE solution, the discriminant of the equation ABOVE has to be equal to 0.
The discriminant is:
\(b^2-4ac\)
We plug in values.
\((-a)^2-4(a)=0\)
We have:
\(a^2-4a=0\)
We factor:
\(a(a-4)=0\)
a = 0 or a = 4
So the sum of the values is 0 + 4 = \(\boxed{4}\)
+2863 It intersects one time if they have ONE solution.
We substitute Y.
\(x^2+a=ax\)
Then we set it equal 0 so it matches the standard quadratic form.
\(x^2-ax+a=0\)
In order to find when it has ONE solution, the discriminant of the equation ABOVE has to be equal to 0.
The discriminant is:
\(b^2-4ac\)
We plug in values.
\((-a)^2-4(a)=0\)
We have:
\(a^2-4a=0\)
We factor:
\(a(a-4)=0\)
a = 0 or a = 4
So the sum of the values is 0 + 4 = \(\boxed{4}\)
