The vertex is ##=(3,4)##

Let’s rewrite the equation and complete the squares

##y=5x^2-30x+49= 5(x^2-6x)+49## ##=5(x^2-6x+9)+49-45## ##=5(x-3)^2+4##

graph{5x^2-30x+49 [-12.18, 13.14, -0.18, 12.47]}