3. The quadratic function $f(x)$ reaches its minimum value of -2 at $x=1$. Determine $f(x)$ such that $f(-3)+4 f(0)=0$. Calculate $f(1+\sqrt{5})$.
3. The quadratic function equation $y=a(x-1)^{2}-2$ ..... 1 point
Data recorded and substituted: for $f(-3)=16 \cdot a-2$ ..... 1 point
for $4 \cdot f(0)=4(a-2)$ ..... 1 point
Equation written $16 \cdot a-2+4(a-2)=0$ ..... 0.5 points
Calculation $a=\frac{1}{2}$ ..... 1 point
Quadratic function written $f(x)=\frac{1}{2}(x-1)^{2}-2$ or $f(x)=\frac{1}{2} x^{2}-x-\frac{3}{2}$ ..... 0.5 points
Calculation $f(1+\sqrt{5})=\frac{1}{2}$ ..... 1 point