Find the coordinates of the vertex of the function 𝑓 of 𝑥 equals negative eight 𝑥 minus six plus four 𝑥 squared.
First, we’ll put the function in standard form, so four 𝑥 squared minus eight 𝑥 minus six. The vertex of a function is ℎ, 𝑘; ℎ is found by taking negative 𝑏 and dividing by two 𝑎 and then 𝑘 is found by taking 𝑓 of ℎ, so plugging ℎ into the function.
So ℎ is negative 𝑏 over two 𝑎. Four is 𝑎, negative eight is 𝑏, and negative six is 𝑐. So we have negative one times negative eight divided by two times four, which is eight over eight which is one. So ℎ is one.
So 𝑘 is equal to 𝑓 of ℎ. And since ℎ is one, let’s plug in one. So we have four times one squared minus eight times one minus six, which is negative 10. Therefore, the coordinate of the vertex is one negative 10.