georgiapage1
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Does anyone have any ideas on how to answer this question? Any help at all is greatly appreciated!
"The quadratic graph ๐‘ฆ = ๐‘Ž๐‘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.
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RDKGames
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(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‘Ž๐‘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: -4 = a(3)^2 + b(3) + c

(B) This is a minimum point, hence the gradient of the curve at x=3 is zero, ie 2a(3) + b = 0

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


You got three equations in three variables. Solve for them.
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David Getling
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(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‘Ž๐‘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.
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georgiapage1
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(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: -4 = a(3)^2 + b(3) + c

(B) This is a minimum point, hence the gradient of the curve at x=3 is zero, ie 2a(3) + b = 0

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


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