In the 𝑥𝑦 plane, the point four, eight lies on the graph of the function 𝑓 of 𝑥 equals two 𝑥 squared minus 𝑚𝑥 plus 16. What is the value of 𝑚?
If the point four, eight lies on the graph of this function, then we can plug in the value of four for 𝑥 and eight for 𝑓 of 𝑥. 𝑓 of 𝑥 equals two 𝑥 squared minus 𝑚𝑥 plus 16. And 𝑓 of four equals eight. And that means eight will equal two times four squared minus 𝑚 times four plus 16. Four squared equals 16. We’ll have two times 16 minus four 𝑚 plus 16. Two times 16 equals 32. Combining like terms, we can add 32 and 16, which is 48. 48 minus four 𝑚 equals eight.
From there, we subtract 48 from both sides. Eight minus 48 is negative 40. 48 minus 48 equals zero. That means negative 40 equals negative four 𝑚. And so, we divide both sides of the equation by negative four. Negative 40 divided by negative four is positive 10. And negative four 𝑚 divided by negative four equals 𝑚. Under these conditions, 𝑚 equals 10. And so, the function 𝑓 of 𝑥 equals two 𝑥 squared minus 10𝑥 plus 16.