Shifting a parabola vs changing slope of a line

[LearninDaMath]

Consider the graphs of two equations:

[y = x] and [y = x^2]


One is a line and the other is a parabola.

If I include a 10x into each formula, to make:

[y = 10x] and [y = 10x + x^2]

then the affect it will have on the line is increase its slope.

But the affect it will have on the parabola is just shift it down and to the right, but not having any affect on its overall curve.

Are all these fair statements?

 

[kscplay]

Consider the graphs of two equations:

[y = x] and [y = x^2]


One is a line and the other is a parabola.

If I include a 10x into each formula, to make:

[y = 10x] and [y = 10x + x^2]

then the affect it will have on the line is increase its slope.

But the affect it will have on the parabola is just shift it down and to the right, but not having any affect on its overall curve.

Are all these fair statements?

Not exactly because you're not doing the same operations on both the equations. You're multiplying 10 for the x^2 and adding 10 for the other. If you had done the same operation on both functions then the outcomes would have also been the same.

 

[e^(i Pi)+1=0]

To shift x² to the right by q units, make it (x-q)². To increase its slope, increase the coefficient of x².

 

[LearninDaMath]

Not exactly because you're not doing the same operations on both the equations. You're multiplying 10 for the x^2 and adding 10 for the other. If you had done the same operation on both functions then the outcomes would have also been the same.

Okay, so if I increase the coefficient of x^2, i'll get a steeper curve and if I increase the coefficient of x, i'll get a steeper slope.

Now if I go from f(x) = x^2 to f(x) = 10x + x^2, that shifts the parabola down and to the left. And if I go from f(x) = x to f(x) = 10 + x, that shifts the line someway (in other words, it changes its x and y intercepts), right?