IDNLearn.com helps you find the answers you need quickly and efficiently. Discover reliable and timely information on any topic from our network of knowledgeable professionals.
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
Learn more here: https://brainly.com/question/13723076