Video: Evaluating Quadratic Functions

Given that the function 𝑓(π‘₯) = βˆ’2π‘₯Β² + 10π‘₯ βˆ’ 2, where π‘“βˆΆ ℝ β†’ ℝ , determine 𝑓(3).

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Video Transcript

Given that the function 𝑓 of π‘₯ equals negative two π‘₯ squared plus 10π‘₯ minus two, where the function’s domain and range are all reals, determine 𝑓 of three.

We copy down our function. And note that we’re looking for the function at π‘₯ equals three. So we substitute three for all the 𝑓 values in our function.

Following the order of operations, we first operate three squared which equals nine. And everything else we’ll bring down. From there, we multiply from left to right. Negative two times nine equals negative 18. 10 times three equals 30.

And we’ll bring everything else down. Negative 18 minus two equals negative 20. And we’ll bring down the plus 30. Now we have negative 20 plus 30 which equals 10.

This function at π‘₯ equals three, 𝑓 of three, equals 10.

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