The curve y = x^2 + 2x -3 has roots at (-a,0) and (b,0). It is translated such that is now intersects the y axis at (0,a+1) (at which point the function is decreasing). The minimum point of the new curve lies on the x-axis. Find the equation of the new curve.

PLS HELP ME WITH THIS IM STUCK

PLS HELP ME WITH THIS IM STUCK

Original post by Tejtejtejtej

The curve y = x^2 + 2x -3 has roots at (-a,0) and (b,0). It is translated such that is now intersects the y axis at (0,a+1) (at which point the function is decreasing). The minimum point of the new curve lies on the x-axis. Find the equation of the new curve.

PLS HELP ME WITH THIS IM STUCK

PLS HELP ME WITH THIS IM STUCK

A sketch of the original and translated quadratic would probably help. Finding a is trivial and you want to consider x,y translations such that the new curve has the desired properties or simply write down the equation (which is probably easier).

Original post by mqb2766

A sketch of the original and translated quadratic would probably help. Finding a is trivial and you want to consider x,y translations such that the new curve has the desired properties or simply write down the equation (which is probably easier).

I’ve tried everything I just can’t get myself to solve this.

Original post by Tejtejtejtej

I’ve tried everything I just can’t get myself to solve this.

Can you sketch the quadratic and determine a?

Original post by mqb2766

Can you sketch the quadratic and determine a?

a = 3

Original post by Tejtejtejtej

a = 3

I agree, I take it youve sketched it and know the location of the minimum as well?

So you want an x,y translation so that it passes through (0,4) which is the y intercept and its decreasing at that point. And the minimum occurs on the x-axis. So either think about what the translations are / simply write down the (completed square) quadratic.

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can someone please explain what principle domain is and why the answer is a not c?Maths

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