Vertex form is (y-k) = b(x-h)2 or y = b(x-h)2 + k where (h,k) is the vertex. You get your equation in that form by "completing the square": In this case b is 1.
y = x2+16x -7 = (x2 + 16x +64) -7 - 64
You get the constant term in the square by noting that when
x+a is squared you get x2 +2ax +a2 and that the constant term is 1/2 of the coefficient of the linear term squared. In our case, 16 = 2a, a2 = (8*8) = 64. We then have to subtract 64 in order to not change the equation:
y = (x+8)2 -71
so the vertex is at (-8,-71) If the constant is next to the variable it has the opposite effect. If it is on the opposite side of the equation it has the effect directly. (x+8) shifts the parabola (y =x2) left, -71 shifts it down. The vertex goes from (0,0) to (-8,-71). We check the math by putting -8 into the original equation and get y=-71.
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