Point B is on the graph of the function f(x) = -3x^2. If the x-coordinate of point B is 2, which ordered pair gives the location of point B?
Understand the Problem
The question asks to find the ordered pair that represents the location of point B on the graph of the function f(x) = -3x^2, given that the x-coordinate of point B is 2.
Answer
(2, f(2))
Answer for screen readers
(2, f(2))
Steps to Solve
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Understand the ordered pair notation An ordered pair is written as $(x, y)$ where $x$ is the x-coordinate and $y$ is the y-coordinate. In this problem, the y-coordinate is given by the function $f(x)$.
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Express the ordered pair using the function Since the y-coordinate is given by the function $f(x)$, the ordered pair can be written as $(x, f(x))$.
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Substitute the given x-coordinate We are given that the x-coordinate of point B is 2. Substituting $x = 2$ into the ordered pair $(x, f(x))$ gives us $(2, f(2))$.
(2, f(2))
More Information
The ordered pair (2, f(2)) represents the point B on the graph of the function f(x) = -3x² when x = 2. The y-coordinate is the value of the function f(x) when x = 2. We can calculate it, $f(2) = -3(2^2) = -3(4) = -12$. Therefore, the coordinates of point B are (2, -12).
Tips
A common mistake involves confusing the x and y coordinates or misinterpreting the function notation.
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