Final answer:
The quadratic function in question is given in vertex form, which reveals its vertex at (-3, 5), and since the coefficient a is positive, the parabola opens upwards. The quadratic formula is generally used for standard form equations, not necessary for vertex form equations like this one.
Step-by-step explanation:
The quadratic function given is f(x)=2(x+3)²+5. To understand this function, let's recognize that it is written in vertex form, where the equation of a quadratic is given as f(x)=a(x-h)²+k, with the vertex at the point (h, k). In this case, the vertex would be (-3, 5) since the function can be seen as f(x)=2[(x-(-3))²]+5. The coefficient 'a' determines the direction of the parabola, which in this case is positive, meaning the parabola opens upwards. This function does not easily lend itself to the quadratic formula, which is generally used to find the roots of quadratics in the standard form ax²+bx+c=0, because it's already in a form that indicates important characteristics such as the vertex.