# Find the equation of a curve with a given turning point

Watch
Announcements

dthomas86

Badges:
3

Rep:

?
You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#1

Hey everyone, I've been tearing my hair out with this question I'm really not sure what you are meant to do and my book has not explained it anywhere how to solve such a question.

Question: Each curve shown is quadratic of the form y = x^2 + bx + c and the turning point is shown (in this case the turning point is (2,3) ). Find the equation of each curve.

Possible answer: Do I substitute in the value of x and y (in this case x=2, y=3) into the equation y = x^2 +bx + c to get 3 = 2^ + 2b + c (although I thought c would be 3 as this is the point where the curve crosses the y-axis? So I would get y= 2^2 + 2b + 3).

Any further help I'll greatly appreciate it. Cheers everyone!!

Question: Each curve shown is quadratic of the form y = x^2 + bx + c and the turning point is shown (in this case the turning point is (2,3) ). Find the equation of each curve.

Possible answer: Do I substitute in the value of x and y (in this case x=2, y=3) into the equation y = x^2 +bx + c to get 3 = 2^ + 2b + c (although I thought c would be 3 as this is the point where the curve crosses the y-axis? So I would get y= 2^2 + 2b + 3).

Any further help I'll greatly appreciate it. Cheers everyone!!

0

reply

Indeterminate

Badges:
3

Rep:

?
You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#2

Report

#2

(Original post by

Hey everyone, I've been tearing my hair out with this question I'm really not sure what you are meant to do and my book has not explained it anywhere how to solve such a question.

Question: Each curve shown is quadratic of the form y = x^2 + bx + c and the turning point is shown (in this case the turning point is (2,3) ). Find the equation of each curve.

Possible answer: Do I substitute in the value of x and y (in this case x=2, y=3) into the equation y = x^2 +bx + c to get 3 = 2^ + 2b + c (although I thought c would be 3 as this is the point where the curve crosses the y-axis? So I would get y= 2^2 + 2b + 3).

Any further help I'll greatly appreciate it. Cheers everyone!!

**dthomas86**)Hey everyone, I've been tearing my hair out with this question I'm really not sure what you are meant to do and my book has not explained it anywhere how to solve such a question.

Question: Each curve shown is quadratic of the form y = x^2 + bx + c and the turning point is shown (in this case the turning point is (2,3) ). Find the equation of each curve.

Possible answer: Do I substitute in the value of x and y (in this case x=2, y=3) into the equation y = x^2 +bx + c to get 3 = 2^ + 2b + c (although I thought c would be 3 as this is the point where the curve crosses the y-axis? So I would get y= 2^2 + 2b + 3).

Any further help I'll greatly appreciate it. Cheers everyone!!

If

then

is the turning point

2

reply

dthomas86

Badges:
3

Rep:

?
You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#3

0

reply

dthomas86

Badges:
3

Rep:

?
You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#4

Indeterminate

Badges:
3

Rep:

?
You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#5

Report

#5

(Original post by

So do I need to complete the square for y = x^2 + bx + c???

Posted from TSR Mobile

**dthomas86**)So do I need to complete the square for y = x^2 + bx + c???

Posted from TSR Mobile

In your case,

Should be easy now

0

reply

HenryD

Badges:
12

Rep:

?
You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#6

Report

#6

Hint: The gradient at each of this point on all the graphs will be 0. So dy/dx=0. If you've done differentiation then you should be able to go from there

0

reply

Badges:
3

Rep:

?
You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#7

Sorry guys I'm being dull I haven't really come across differentiation yet as its quite early on in the book.

The answer in the book is y = x^2 - 4x + 7

I still don't know how to get this answer.

Posted from TSR Mobile

The answer in the book is y = x^2 - 4x + 7

I still don't know how to get this answer.

Posted from TSR Mobile

0

reply

Indeterminate

Badges:
3

Rep:

?
You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#8

Report

#8

(Original post by

Sorry guys I'm being dull I haven't really come across differentiation yet as its quite early on in the book.

The answer in the book is y = x^2 - 4x + 7

I still don't know how to get this answer.

Posted from TSR Mobile

**dthomas86**)Sorry guys I'm being dull I haven't really come across differentiation yet as its quite early on in the book.

The answer in the book is y = x^2 - 4x + 7

I still don't know how to get this answer.

Posted from TSR Mobile

Note that (a,b)

is the turning point of the equation

What are a and b in your case?

Now expand the brackets

0

reply

Albino

Badges:
11

Rep:

?
You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#9

Report

#9

**dthomas86**)

Sorry guys I'm being dull I haven't really come across differentiation yet as its quite early on in the book.

The answer in the book is y = x^2 - 4x + 7

I still don't know how to get this answer.

Posted from TSR Mobile

0

reply

HenryD

Badges:
12

Rep:

?
You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#10

Report

#10

**dthomas86**)

Sorry guys I'm being dull I haven't really come across differentiation yet as its quite early on in the book.

The answer in the book is y = x^2 - 4x + 7

I still don't know how to get this answer.

Posted from TSR Mobile

0

reply

Badges:
3

Rep:

?
You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#11

How did you get the equation (x - a)^2 + b^2 in the first place? Where did the coefficient a come from and what happened to c?

Sorry guys its been a long day and it hasn't been clearly explained in the book how to tackle such a question. Cheers.

Posted from TSR Mobile

Sorry guys its been a long day and it hasn't been clearly explained in the book how to tackle such a question. Cheers.

Posted from TSR Mobile

0

reply

ecw412

Badges:
0

Rep:

?
You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#12

Report

#12

(Original post by

How did you get the equation (x - a)^2 + b^2 in the first place? Where did the coefficient a come from and what happened to c?

Sorry guys its been a long day and it hasn't been clearly explained in the book how to tackle such a question. Cheers.

Posted from TSR Mobile

**dthomas86**)How did you get the equation (x - a)^2 + b^2 in the first place? Where did the coefficient a come from and what happened to c?

Sorry guys its been a long day and it hasn't been clearly explained in the book how to tackle such a question. Cheers.

Posted from TSR Mobile

0

reply

Badges:
3

Rep:

?
You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#13

Yeah I know how to complete the square would I get: (x + b/2 )^2 - (b/2)^2 + c if I completed the square for the quadratic y = x^2 + bx + c

Posted from TSR Mobile

Posted from TSR Mobile

0

reply

FO12DY

Badges:
13

Rep:

?
You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#14

Badges:
3

Rep:

?
You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#15

Without using differentiation could you show me how to solve it by completing the square? Cheers

Posted from TSR Mobile

Posted from TSR Mobile

0

reply

FO12DY

Badges:
13

Rep:

?
You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#16

Report

#16

(Original post by

Without using differentiation could you show me how to solve it by completing the square?

**dthomas86**)Without using differentiation could you show me how to solve it by completing the square?

/if not, why do you want to avoid differentiation?

0

reply

Badges:
3

Rep:

?
You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#17

Because the chapter in the book I have got is about completing the square.

I'm not sure why a question like that is in the book so early on. As I haven't touched on differentiation yet.

Do you know how to solve it by completing the square?

Posted from TSR Mobile

I'm not sure why a question like that is in the book so early on. As I haven't touched on differentiation yet.

Do you know how to solve it by completing the square?

Posted from TSR Mobile

0

reply

Mark85

Badges:
16

Rep:

?
You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#18

Report

#18

(Original post by

Yeah I know how to complete the square would I get: (x + b/2 )^2 - (b/2)^2 + c if I completed the square for the quadratic y = x^2 + bx + c

Posted from TSR Mobile

**dthomas86**)Yeah I know how to complete the square would I get: (x + b/2 )^2 - (b/2)^2 + c if I completed the square for the quadratic y = x^2 + bx + c

Posted from TSR Mobile

so if you know the turning point, you know what -b/2 is. Use the other coordinate of the turning point to find c

0

reply

Dualcore

Badges:
0

Rep:

?
You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#19

Report

#19

(Original post by

Because the chapter in the book I have got is about completing the square.

I'm not sure why a question like that is in the book so early on. As I haven't touched on differentiation yet.

Do you know how to solve it by completing the square?

Posted from TSR Mobile

**dthomas86**)Because the chapter in the book I have got is about completing the square.

I'm not sure why a question like that is in the book so early on. As I haven't touched on differentiation yet.

Do you know how to solve it by completing the square?

Posted from TSR Mobile

y=(x+b/2)^2-(b/2)^2+c

As you can see apart from thee the bit in the brackets the other terms are constants in terms of b and c.

You know the turning point is at (2,3), if you think about what the graph looks like the minimum point is where the y is the smallest value it can be and that is where x=2, as anything squared is positive the value of the first term must be zero so ((2)+(b/2))^2=0 therefore ((2)+(b/2))=0, and now we consider the y value at this point, it is 3 so we can say that 3=-(b/2)^2+c, we can use the value of b we calculated before to work this out.

Hope this helped

0

reply

FO12DY

Badges:
13

Rep:

?
You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#20

Report

#20

I only ask because by the time you've covered all the material, I'd wager on you solving it by differentiation without batting an eyelid, without considering completing the square.

0

reply

X

### Quick Reply

Back

to top

to top