f(x)=2x^2+6x-13 find vertex,axis of symmtry

Question

state the concavity, vertex and axis of symmetry for the question

Answer 1

f(x)=2(x²+3x)-13=2(x²+3x+9/4-9/4)-13=

2(x+3/2)²-9/2-13=2(x+3/2)²-35/2.

When x=-3/2, f(x)=-35/2 and this is the minimum value for f(x) because the square term is always positive and is zero only at the vertex, so the vertex is at (-3/2,-35/2). Because the vertex is a minimum the concavity is concave up. The vertex lies on the axis of symmetry, which is x=-3/2.