Find the coordinates of the vertex of the function 𝑓(𝑥) = −8𝑥 − 6 + 4𝑥².
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
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.
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