Chapter 3 - Polynomial and Rational Functions - 3.1 Quadratic Functions and Models - 3.1 Execises - Page 320: 82

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Step 1. Known the vertex at $(5,3)$, we can write the equation as $a(x-5)^2+3=0$ Step 2. Know that $x=2$ is a solution, we have $a(2-5)^2+3=0$ which gives $a=-\frac{1}{3}$ Step 3. The equation becomes $-\frac{1}{3}(x-5)^2+3=0$ which gives solutions $x=5\pm3$ Step 4. The other solution is $x=8$