Video: Finding the Value of the 𝑦-Coordinate of a Point Lying on the Curve of a Given Quadratic Function

Find 𝑦, given that the point (βˆ’2, 𝑦) lies on the function 𝑓(π‘₯) = βˆ’6π‘₯Β² βˆ’ 10π‘₯ + 8.

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Video Transcript

Find 𝑦 given that the point negative two 𝑦 lies on the function 𝑓 of π‘₯ equals negative six π‘₯ squared minus 10π‘₯ plus eight.

Let’s firstly replace 𝑓 of π‘₯ with 𝑦 so we can rewrite the equation 𝑦 equals negative six π‘₯ squared minus 10π‘₯ plus eight.

Substituting in the π‘₯-coordinate negative two gives us 𝑦 equals negative six multiplied by negative two squared minus 10 multiplied by negative two plus eight. Negative two squared is negative two multiplied by negative two, which gives us positive four.

Therefore, negative six multiplied by positive four is negative 24. Negative 10 multiplied by negative two is positive 20. This leaves us with the equation 𝑦 equals negative 24 plus 20 plus eight.

Negative 24 plus 20 is negative four. Adding eight to this gives us an answer of 𝑦 equals positive four. Therefore, the value of 𝑦 given that the point negative two 𝑦 lies on the function 𝑓 of π‘₯ equals negative six π‘₯ squared minus 10π‘₯ plus eight is 𝑦 equal to four.

Alternatively, we could say that the point negative two, four lies on the function 𝑓 of π‘₯.

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