I would like to show that this function
$$2x^2 + 8y^2$$
is convex or concave by using the definition
$$f(θx+(1−θ)y) \le θf(x)+(1−θ)f(y)$$
From my understanding, using the Hessian matrix, I believe for certain I can show that the function is positive definite and hence convex.
But I'm not certain how to proceed on showing this using the equation shown above.