what is the coordinate of the vertex of the graph of y=x^2+8x+1

Question

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Answer 1

y=x²+8x+1, which can be written y=x²+8x+16-16+1, which is y=(x+4)²-15. From this it can be seen that the minimum value of y is -15, the lowest point on the curve, which is the vertex. This occurs when x=-4.

We can write this as y+15=(x+4)² which is the vertex form of the equation and the vertex is at (-4,-15).