Maths parabola minimum point?

Hi,
I am a GCSE maths student, and I need some help with a parabola minimum point question I was doing for revision.
When a question asks 'find the minimum point' and gives you the equation of the parabola, what do you do after you complete the square?

For example, the question used the equation x squared - 8x +23

I then wrote this out as (x-4) squared + 7

Does this mean that y=7 and x=-4 ? Or do I put it into the first equation?

(edited 11 years ago)

Reply 1

james.h

11

Original post by katesimpson2112

Hi,
I am a GCSE maths student, and I need some help with a parabola minimum point question I was doing for revision.
When a question asks 'find the minimum point' and gives you the equation of the parabola, what do you do after you complete the square?

For example, the question used the equation x squared - 8x +23

I then wrote this out as (x-4) squared + 7

Does this mean that y=7 and x=-4 ? Or do I put it into the first equation?

Almost, check the sign on your x-value.

The smallest value (x-4)² can take is zero, since squared numbers are always positive. So you can immediately see that the minimum point, y=7, will be where the squared bracket is zero, i.e: where x-4=0.

:smile:

Reply 2

katesimpson2112

OP

So do you mean that:
If x-4=0, then x=4 ? And y=7?
Sorry, I just get a tad frustrated due to my slightly incompetant teacher who didn't finish teaching us the syllabus :L

Reply 3

Brand New Eyes

2

Original post by katesimpson2112

So do you mean that:
If x-4=0, then x=4 ? And y=7?
Sorry, I just get a tad frustrated due to my slightly incompetant teacher who didn't finish teaching us the syllabus :L