# Video: Finding the Vertex of Quadratic Functions and Whether It Is Maximum or Minimum

Find the coordinates of the vertex of the graph of π(π₯) = π₯Β² β 6π₯ β 4. State the value of the function at the vertex and determine whether it is a maximum or minimum.

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### Video Transcript

Find the coordinates of the vertex of the graph of π of π₯ equals π₯ squared minus six π₯ minus four. State the value of the function at the vertex and determine whether it is a maximum or minimum.

For any parabola, π of π₯ equals ππ₯ squared plus bπ₯ plus π and the vertex β, π can be found using β equals negative π over two π and π equals π of β. So if this is our function, π equals one, π equals negative six, and π equals negative four. So to find the vertex β, π, we will find β by negative π over two π. So here, we will multiply negative one times negative six over two times one, which is six over two, which is equal to three. So that is β.

So now we need to find π. And π is equal to π of β. We have to plug in the value of β into our function. So itβs equal to π of three. So we will take our function and plug in three. And we get negative 13. So the vertex is three, negative 13.

So now we have to decide if itβs a minimum or maximum value. Since π is a positive leading coefficient, our graph should open upward. So our vertex will be at the bottom which means it would be a minimum.

Therefore, the vertex again is three, negative 13. The value of the function at the vertex is negative 13. And itβs a minimum value.