gradient generalisation

[red and white kop!]

make a generalisation about the gradient at any point on the graph of y=x^2 + c, where c is any real number

my textbook gives no answer for this, so i'd just like to make sure that the correct answer is that all gradients of curves of this form behave identically to those of y=x^2, i.e. modulus of gradient increases with modulus of x, negative to the left of y-axis and positive to the right of the y-axis, am i correct?

 

[Deleted member 4993]

make a generalisation about the gradient at any point on the graph of y=x^2 + c, where c is any real number

my textbook gives no answer for this, so i'd just like to make sure that the correct answer is that all gradients of curves of this form behave identically to those of y=x^2, i.e. modulus of gradient increases with modulus of x, negative to the left of y-axis and positive to the right of the y-axis, am i correct?

I would say that the "modulus of the gradient" refers to the "slope of the tangent" of the lines. Then My statement would be that the slope would be constant for the family of curves (for different 'c's) for a given absissa (x).