Video Transcript
Find the value of 𝑐 given the function 𝑓 of 𝑥 equals 𝑥 squared plus 𝑐 passes through the point seven, eight.
We’re given the point seven, eight and told that it passes through this function, 𝑓 of 𝑥 equals 𝑥 squared plus 𝑐. First, we need to think about what this point represents. A point given like this is in the form 𝑥-coordinate, 𝑦-coordinate. And the 𝑦-coordinate is equal to the function evaluated at a certain 𝑥, the 𝑓 of 𝑥. And that means, to solve, we’ll plug the value eight in for 𝑓 of 𝑥. And then we’ll plug the value seven in for 𝑥.
Our new statement says eight equals seven squared plus 𝑐. Seven squared is 49. Eight is equal to 49 plus 𝑐. To solve for 𝑐, we subtract 49 from both sides of the equation. And we get negative 41 equals 𝑐. Since that’s true, we plug in negative 41 for the 𝑐 variable. And we see that the function is 𝑓 of 𝑥 is equal to 𝑥 squared minus 41. And the constant value we were looking for, 𝑐, is negative 41.
