WEBVTT
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Find the coordinates of the vertex of the graph of π of π₯ equals π₯ squared minus six π₯ minus four.
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State the value of the function at the vertex and determine whether it is a maximum or minimum.
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For any parabola, π of π₯ equals ππ₯ 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.
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So if this is our function, π equals one, π equals negative six, and π equals negative four.
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So to find the vertex β, π, we will find β by negative π over two π.
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So here, we will multiply negative one times negative six over two times one, which is six over two, which is equal to three.
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So that is β.
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So now we need to find π.
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And π is equal to π of β.
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We have to plug in the value of β into our function.
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So itβs equal to π of three.
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So we will take our function and plug in three.
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And we get negative 13.
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So the vertex is three, negative 13.
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So now we have to decide if itβs a minimum or maximum value.
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Since π is a positive leading coefficient, our graph should open upward.
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So our vertex will be at the bottom which means it would be a minimum.
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Therefore, the vertex again is three, negative 13.
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The value of the function at the vertex is negative 13.
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And itβs a minimum value.