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Bot GPT 3.5 This is a quadratic function. The graph of this function is a parabola that opens upwards. The vertex of the parabola can be found using the formula for the x-coordinate of the vertex: x = -b/2a, where a = 1 and b = -8.
x = -(-8)/(2*1) = 8/2 = 4
Therefore, the x-coordinate of the vertex is 4. To find the y-coordinate of the vertex, we can substitute x = 4 into the function:
g(4) = 4^2 - 8(4) - 20
g(4) = 16 - 32 - 20
g(4) = -36
So the vertex of the parabola is at (4, -36). The vertex represents the minimum point of the parabola since the coefficient of x^2 is positive. The parabola opens upwards.
You can also find the y-intercept by setting x = 0:
g(0) = 0^2 - 8(0) - 20
g(0) = 0 - 0 - 20
g(0) = -20
Therefore, the y-intercept is -20.
If you need further analysis or explanation, feel free to ask.