Find-the-range-of-this-function-x-2-13x-36-0-Help-

Question Number 187651 by Mastermind last updated on 19/Feb/23

Find the range of this function

x^{2} - 13 x + 36 = 0

Help!

Answered by Ar Brandon last updated on 19/Feb/23

Let y = x^{2} - 13 x + 36

\Rightarrow x^{2} - 13 x + 36 - y = 0

\Rightarrow x = \frac{13 \pm \sqrt{169 - 4 (36 - y)}}{2}

= \frac{13 \pm \sqrt{25 + 4 y}}{2}

25 + 4 y ⩾ 0 \Rightarrow y ⩾ - \frac{25}{4}

Hence range f (x) ⩾ - \frac{25}{4}

Commented by Mastermind last updated on 20/Feb/23

Thank you BOSS, {that}^{'} s what i also

got but with diff . method .

Answered by mr W last updated on 20/Feb/23

x^{2} - 13 x + 36

= {(x - \frac{13}{2})}^{2} + 36 - {(\frac{13}{2})}^{2}

⩾ 36 - {(\frac{13}{2})}^{2} = - \frac{25}{4}

\Rightarrow r a n g e i s [- \frac{25}{4}, + \infty)

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