I don't know how to approach this quesion... Core 3! Watch

J DOT A
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Report Thread starter 7 years ago
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Hey guys

Well the question asks,

1) The function y=x^2-4ax where a is a positive constant is defined for all real values of x. Given that the range is y>=-7, find the exact value of a.

Now to find the range from a quadratic expression, we use completing square right? How do I complete the square of the above equation?
Is there another method I could use? I tried to differentiate y=x^2-4ax, and eqaute the differential to 0 to get a stationary point... however I get

x=a/2
and if I plug this in the original equation I don't get a feasiable answer.
The answer is (*sqrt7)/2

Can someone tell me how they got to this answer please?
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J DOT A
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Report Thread starter 7 years ago
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Okay guys I got the answer!

But I want to ask why I put -7=x^2-4ax?
and then use the discriminant?

Why do I use the discriminant and put -7=x^2-4ax?
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Gemini92
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(Original post by J DOT A)
Okay guys I got the answer!

But I want to ask why I put -7=x^2-4ax?
and then use the discriminant?

Why do I use the discriminant and put -7=x^2-4ax?
As you said in the first post, you differentiate the equation to get the x co-ordinate of the stationary point in terms of a. (Its x=2a, not x=a/2)

Since the range of y values is y>=-7 and the graph is a parabola with a minimum, the y co-ordinate of the minimum must be -7.

You then substitute y=-7 and x=2a into the original equation and solve to get a.
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