How is the graph of g(x)=-12+x^2 related to the graph of f(x)=x^2?

2 Answers
Jan 24, 2018

See below.

Explanation:

If we have a function f(x)=x^2 and add a constant c to it .i.e.

f(x)=x^2+c

If c>0

The curve of f(x)=x^2 is translated c units in the positive y direction.

If c<0

The curve of f(x)=x^2 is translated c units in the negative y direction.

So:

g(x)=-12+x^2=x^2-12

c=-12 :. c<0

Therefore:

g(x)=x^2-12color(white)(888) is:

f(x)=x^2 translated 12 units in the negative y direction.

This is the graph of both f(x) and g(x)

enter image source here

Jan 24, 2018

See explanation

Explanation:

You plot the graph of y=x^2 and lower the whole thing by 12

This is how it works mathematically

In that: given y_1=x^2" "....................Equation(1)

Subtract 12 from both sides

color(green)(color(red)(y_1-12)=x^2-12)" "........................Equation(2)

Set color(red)(color(purple)(y_2)=y_1-12) and substitute into Eqn(2) giving

color(purple)(y_2)color(green)(=x^2-12)" "..............................Equation(2_a)