Wierzchołek paraboli która jest wyrazem funkcji f(x)= ax^2+24x-9, należy do prostej o równaniu y=3. .... Question from @KikixOx

December 2018 1 5 Report

Wierzchołek paraboli która jest wyrazem funkcji f(x)= ax^2+24x-9, należy do prostej o równaniu y=3. Znajdź miejsce zerowe funkcji f.

Cyna4 Witaj.

$f(x)=ax^{2}+24x-9\\\\q=3\\\\p=\frac{-b}{2a_{w}}=\frac{-24}{2a}=-\frac{12}{a}\\\\q=f(p)=a\cdot(-\frac{12}{a})^{2}+24\cdot(-\frac{12}{a})-9=\frac{144}{a}-\frac{288}{a}-9=-\frac{144}{a}-9\\\\-\frac{144}{a}-9=3\\\\\frac{144}{a}=-12\\\\a=-12$

Miejsce zerowe:

$f(x)=-12x^{2}+24x-9\\\\f(x)=0\\\\-12x^{2}+24x-9=0\\\\12x^{2}-24x+9=0\\\\4x^{2}-8x+3=0\\\\\Delta=(-8)^{2}-4\cdot4\cdot3=64-48=16\\\\\sqrt{\Delta}=4\\\\x_{1}=\frac{4+8}{8}=\frac{12}{8}=\frac{3}{2}\\\\x_{2}=\frac{-4+8}{8}=\frac{4}{8}=\frac{1}{2}\\\\x_{0}\in\{\frac{1}{2};\frac{3}{2}\}$

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