Oxford pat math problem

3

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

Reply 1

mqb2766

21

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

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).

Reply 2

Tejtejtejtej

OP

3

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.

Reply 3

mqb2766

21

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?

Reply 4

Tejtejtejtej

OP

3

Original post by mqb2766

Can you sketch the quadratic and determine a?

a = 3

Reply 5

mqb2766

21

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.

Oxford pat math problem

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