Show all steps to determine the vertex for y= x2 - 6x+2

The vertex of the given conic section is (3, -7)

Step-by-step explanation:

The function given represents a parabola which is part of the family of conic sections. The vertex of a parabola represents the turning point of the curve, that is the slope of the line passing through the vertex is 0.

We first determine the gradient function of the curve by applying differential calculus. We differentiate the function with respect to x then set the result to 0;

dy/dx = 2x - 6; the gradient function.

Setting to 0 and solving for x;

2x - 6=0

2x = 6

x = 3

Lastly, we substitute x =3 in the equation to determine the y-value;

y = 3^2 -6(3)+2

y = -7

The vertex of the parabola is thus;

(3, -7)

See the attachment below

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