Math CentralQuandaries & Queries


Question from Rita, a student:

If (2, b) is a point on the graph of y = (x^2) + 4x, find the value of b.

Hi Rita,

In order for any ordered pair (x, y) to be a point on the graph of a function or relation, the values of x and y must satisfy the equation. This means that when the values are substituted into the equation, you get a true equality statement.

For example, (3, -5) lies on the graph of y = -2x + 1 because by substitution we get
-5 = -2(3) + 1
-5 = -6 + 1
-5 = -5 which is a true equality statement

Similarly, (3, -5) does NOT lie on the graph of y = 4x + 3 because by substitution we get
-5 = 4(3) + 3
-5 = 12 + 3
-5 = 15 which is NOT a true equality statement

In your question, simply substitute your x value of 2 into the equation, and exchange y with "b".
Now what value must "b" have in order to get a true equality statement?

Hope this helps,

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