Alternative way to verify a function of $\mathbb R^2$ is strictly convex?

Question

How can I see that this function $f(x,y)=(x-9/4)^2+(y-2)^2$ is strictly convex?

I already calculate the Hessian matrix but I found that $f$ it's just convex.

I also know that I can use the definition of strongly quasiconvex $(x,y\in\mathbb R^n,f(\lambda x+(1-\lambda)y)<\max\{f(x),f(y)\})$ to see that $f$ is strictly convex, but as is definition, the calculations would be very tedious.

Is there an easier way to know $f(x,y)=(x-9/4)^2+(y-2)^2$ is strictly convex?

Thanks in advance for your help.

Answer 1

We have that

• $f_{xx}=2$
• $f_{yy}=2 $
• $f_{xy}=0$

then consider the hessian matrix which is positive definite and thus $f$ is strictly convex.