Video: Finding the Value of the Constant in a Quadratic Function given Its Vertex Coordinates

The figure below represents the function 𝑓(π‘₯) = π‘₯Β² + π‘š. Find the value of π‘š given the length of 𝑂𝐴 is 4 units.

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Video Transcript

The figure below represents the function 𝑓 of π‘₯ equals π‘₯ squared plus π‘š. Find the value of π‘š, given the length of 𝑂𝐴 is four units.

So here is the equation of our function. Since our leading term is an π‘₯ squared, this must be a quadratic which looks something like this, just like our graph. Now the plus π‘š, this will shift our graph up and down. So the parent function, the original function, just 𝑓 of π‘₯ equals π‘₯ squared where π‘š is just zero, the vertex is at the point zero, zero.

So looking at our figure, it’s been moved down four units. And we also know this because the length of 𝑂𝐴 is four units. So if we went down four, π‘š must be negative four. Therefore, π‘š equals negative four would be our final answer.

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