Shayan A.

asked • 04/10/17# Find the set of values of k for which f(x)= 3x^2 -5x -k is greater than 1 for all real x

This is a year 11 methods question about applying function notation.

Could someones please explain the question and then give me a working out for it?

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## 1 Expert Answer

Roman C. answered • 04/10/17

Masters of Education Graduate with Mathematics Expertise

The minimum (or maximum) value achieved for y = ax

^{2}+ bx + c is y = -Δ/(4a) where Δ = b^{2}- 4ac is the discriminant.In your case:

Δ = b

^{2}- 4ac = (-5)^{2}- 4(3)(-k) = 25 + 12ky

_{min}= -(25 + 12k)/(4·3) = -25/12 - k-25/12 - k > 1

25/12 + k < -1

k < -1 - 25/12

k < -37/12

Shayan A.

Thank you for your response,

I was just wondering where does the y=-(discriminant)/4a comes from?

Whats the reason that it works?

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04/10/17

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Prentice D.

^{2}+bx+c (happy face graph due to positive a value), the function will have a lowest point when the derivative of this function is equal to zero. So,^{2}-5x -k04/10/17