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Video: Finding the Coordinates of the Vertex of a Quadratic Function

Bethani Gasparine

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

00:57

Video Transcript

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.