# Thread: Equation of graph after transforming

1. ## Equation of graph after transforming

The equation of a graph is: y = -x^2 + x + 2. I had to find the equation by looking at the graph. I have cross checked and found the equation is correct.
Problem: the graph of this parabola is moved 2 units to the left and 3 units up. Give the equation of the parabola in the new position, in simplified form, and also give the y-intercept.

Answer: By looking at the graph and shifting the points, I found the y-intercept to be 3. How will I write the new equation?

2. ## Re: Equation of graph after transforming

Originally Posted by hsetima
The equation of a graph is: y = -x^2 + x + 2. I had to find the equation by looking at the graph. I have cross checked and found the equation is correct.
Problem: the graph of this parabola is moved 2 units to the left and 3 units up. Give the equation of the parabola in the new position, in simplified form, and also give the y-intercept.

Answer: By looking at the graph and shifting the points, I found the y-intercept to be 3. How will I write the new equation?
for any function y = f(x)

shift 2 units left ...

y = f(x+2)

shift 3 units up ...

y = f(x+2) + 3

3. ## Re: Equation of graph after transforming

Take the easy example of

$f(x)=x^2$ here.

$f(x-1)=(x-1)^2=x^2-2x+1$. How does this change the graph?

$f(x)-1=x^2-1$ How does this change the graph?

$f(x-1)-1=x^2-2x$ which does this to the graph expectedly.

You have: $f(x)=-x^2+x+2$.

Can you spot the relation?

Edit: Was beaten to it.

4. ## Re: Equation of graph after transforming

Thanks everybody,
problem solved!