what's the axis of symetry, vertex, and graph y=2x^2+6x-1

Question

please graph, show the axis of symetry, and the vertex of y= 2x^2+6x-1

Answer 1

y=2x²+6x-1=2(x²+3x)-1=

2(x²+3x+9/4-9/4)-1=

2(x+3/2)²-9/2-1=

2(x+3/2)²-11/2.

When x=-3/2 y=-11/2, the minimum value for the curve since the square term makes y more positive for all values of x different from -3/2. So the vertex is at (-3/2,-11/2). The axis of symmetry is x=-3/2.