Answer
$\frac{1}{2}x^2-\frac{7}{2}x+5$
Work Step by Step
Step 1. Assume the quadratic function has the form $f(x)=a(x-x_1)(x-x_2)$
Step 2. Given the two x-intercepts, we have $x_1=2, x_2=5$
Step 3. Given the y-intercept, we have $f(0)=5$ or $a(0-2)(0-5)=5$ which gives $a=\frac{1}{2}$
Step 4. Thus the function is $f(x)=\frac{1}{2}(x-2)(x-5)=\frac{1}{2}x^2-\frac{7}{2}x+5$
