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 𝑎 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.