Get the equation y = x² - 8x + 7 in vertex form y = (x - h)² + k

Put the equation y = x² - 8x + 7 in the form y = (x - h)² + k

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y = a(x - h)² + k is “vertex form” for a quadratic equation, where a is the stretch or compression,
h is the x-coordinate of the vertex, and k is the y-coordinate of the vertex.

You can get there by completing the square.

Take half of the coefficient of x, square it, then add it and subtract it all from the right side.
y = x² - 8x + 7
y = x² - 8x + 16 + 7 - 16  {took half of -8, got 4, squared it, got 16….then added and subtracted 16 from right side}
y = (x - 4)² - 9  {factored the x² - 8x + 16 into (x - 4)², also combined 7 and -16}

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