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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?
 

 Nov 12, 2019

Best Answer 

 #1
avatar+2551 
+3

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 = \(\boxed{4}\)

.
 Nov 12, 2019
 #1
avatar+2551 
+3
Best Answer

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 = \(\boxed{4}\)

CalculatorUser Nov 12, 2019

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