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f(x)=9x^(2)-60 x+80

f(x)=9x2−60x+80f(x)=9x^{2}-60x+80

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Full solution

Q. f(x)=9x2−60x+80f(x)=9x^{2}-60x+80
  1. Identify coefficients: Identify the coefficients of the quadratic equation f(x)=9x2−60x+80f(x) = 9x^2 - 60x + 80.\newline- a=9a = 9, b=−60b = -60, c=80c = 80
  2. Find vertex x-coordinate: Use the vertex formula x=−b2ax = -\frac{b}{2a} to find the x-coordinate of the vertex.\newline- x=−−602⋅9x = -\frac{-60}{2\cdot 9}\newline- x=6018x = \frac{60}{18}\newline- x=103x = \frac{10}{3}
  3. Find vertex y-coordinate: Substitute x=103x = \frac{10}{3} into the function to find the y-coordinate of the vertex.\newline- f(103)=9(103)2−60(103)+80f\left(\frac{10}{3}\right) = 9\left(\frac{10}{3}\right)^2 - 60\left(\frac{10}{3}\right) + 80\newline- f(103)=9(1009)−200+80f\left(\frac{10}{3}\right) = 9\left(\frac{100}{9}\right) - 200 + 80\newline- f(103)=100−200+80f\left(\frac{10}{3}\right) = 100 - 200 + 80\newline- f(103)=−20f\left(\frac{10}{3}\right) = -20

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