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The equation of the function passing through the given point is
y = -8x -1
The equation of a line in point-slope form is expressed as:
[tex]y-y_0=m(x-x_0)[/tex]
m is the slope
[tex](x_0,y_0)[/tex] is the point on the line
Given the equation [tex]y=2x^2-4x+1[/tex]
Get the slope by differentiating at x = -1
[tex]m=\frac{dy}{dx} =4x-4\\m=\frac{dy}{dx} =4(-1)-4\\m=\frac{dy}{dx} =-4-4\\m=\frac{dy}{dx} =-8[/tex]
Substitute (-1, 7) and m = -8 into the formula above to have [tex]y-7=-8(x+1)[/tex]
Simplify
[tex]y-7=-8x-8\\y+8x = -8+7\\y+8x=-1\\y=-8x-1[/tex]
Hence the equation of the function passing through the given point is
y = -8x -1
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