# Maths Quadratic Question

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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 ๐ฆ = ๐๐ฅ^2 + ๐๐ฅ + 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.

"The quadratic graph ๐ฆ = ๐๐ฅ^2 + ๐๐ฅ + 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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(Original post by

Does anyone have any ideas on how to answer this question? Any help at all is greatly appreciated!

"The quadratic graph ๐ฆ = ๐๐ฅ^2 + ๐๐ฅ + 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.

**georgiapage1**)Does anyone have any ideas on how to answer this question? Any help at all is greatly appreciated!

"The quadratic graph ๐ฆ = ๐๐ฅ^2 + ๐๐ฅ + 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.

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.

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**georgiapage1**)

Does anyone have any ideas on how to answer this question? Any help at all is greatly appreciated!

"The quadratic graph ๐ฆ = ๐๐ฅ^2 + ๐๐ฅ + 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.

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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(Original post by

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.

**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.

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