Watch
Announcements
#1
Does anyone have any ideas on how to answer this question? Any help at all is greatly appreciated!
"The quadratic graph ๐ฆ = ๐๐ฅ^2 + ๐๐ฅ + ๐ has a minimum point (3, -4) and passes through (2,-2). Find the values of a, b and c."

I've tried finding the gradient and using y - y1 = m(x - x1) but it gives the incorrect answer. The correct answers are a = 2, b = -12, c = 14 if it helps, I just have no clue how to get there.
0
7 months ago
#2
(Original post by georgiapage1)
Does anyone have any ideas on how to answer this question? Any help at all is greatly appreciated!
"The quadratic graph ๐ฆ = ๐๐ฅ^2 + ๐๐ฅ + ๐ has a minimum point (3, -4) and passes through (2,-2). Find the values of a, b and c."

I've tried finding the gradient and using y - y1 = m(x - x1) but it gives the incorrect answer. The correct answers are a = 2, b = -12, c = 14 if it helps, I just have no clue how to get there.
Why are you constructing the equation of a straight line?

The minimum point is (3,-4) so there are two things to take away from this:

(A) The curve passes through (3,-4), hence we have an equation satisfied by a,b,c:

(B) This is a minimum point, hence the gradient of the curve at is zero, ie

And the curve also passes through (2,-2) hence you get a third equation to be satisfied by a,b,c: .

You got three equations in three variables. Solve for them.
0
7 months ago
#3
(Original post by georgiapage1)
Does anyone have any ideas on how to answer this question? Any help at all is greatly appreciated!
"The quadratic graph ๐ฆ = ๐๐ฅ^2 + ๐๐ฅ + ๐ has a minimum point (3, -4) and passes through (2,-2). Find the values of a, b and c."

I've tried finding the gradient and using y - y1 = m(x - x1) but it gives the incorrect answer. The correct answers are a = 2, b = -12, c = 14 if it helps, I just have no clue how to get there.
Here's the smart way.

From the minimum we know that its formula is y = k(x - 3)2 - 4.
Now substitute in for (2, -2) to get k.
Then expand and collect terms to put the formula into the required form.
1
#4
(Original post by RDKGames)
Why are you constructing the equation of a straight line?

The minimum point is (3,-4) so there are two things to take away from this:

(A) The curve passes through (3,-4), hence we have an equation satisfied by a,b,c:

(B) This is a minimum point, hence the gradient of the curve at is zero, ie

And the curve also passes through (2,-2) hence you get a third equation to be satisfied by a,b,c: .

You got three equations in three variables. Solve for them.
Thank you so much
0
X

new posts
Back
to top
Latest
My Feed

Oops, nobody has postedin the last few hours.

Why not re-start the conversation?

see more

See more of what you like onThe Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Poll

Join the discussion

Current uni students - are you thinking of dropping out of university?

Yes, I'm seriously considering dropping out (29)
18.95%
I'm not sure (3)
1.96%
No, I'm going to stick it out for now (53)
34.64%
I have already dropped out (3)
1.96%
I'm not a current university student (65)
42.48%