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Math Help - Equation of graph after transforming

  1. #1
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    Question 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?
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  2. #2
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    Re: Equation of graph after transforming

    Quote Originally Posted by hsetima View Post
    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
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  3. #3
    Super Member Quacky's Avatar
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    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.
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  4. #4
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    Re: Equation of graph after transforming

    Thanks everybody,
    problem solved!
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