Question

What does increasing the constant c by 3 units in an equation of the form y=x^2+c?

Answer 1

Answer:

A translation of 3 units up (see the explanation)

Step-by-step explanation:

we have

$y=x^{2}+c$

This is a vertical parabola open upward (the leading coefficient is positive)

The vertex is the point (0,c)

If increasing the constant c by 3 units

then

The new equation will be

$y=x^{2}+(c+3)$

The new vertex is the point (0,c+3)

That means

The new parabola is a translation of the original parabola

The rule of the translation is

(x,y) ----> (x,y+3)

The translation is 3 units up