Question

Find the equation of the axis of symmetry and the coordinates of the vertex of the graph of the function

Y=2x^2+12x+13
axis of symmetry:
vertex:

Answer 1

Axis of symmetry: –3

Vertex: (–3, –5)

Explanation:

For a quadratic function in standard form, the axis of symmetry is a vertical line
`x=-(b)/(2a)`. Therefore:

`x=-(b)/(2a)=-(12)/(2(2))=-(12)/(4)=-3`

For the vertex, –3 is the x-coordinate and we solve for y to find the y-coordinate:

y = 2x² + 12x + 13

y = 2(–3)² + 12(–3) + 13

y = 2(9) + 12(–3) + 13

y = 18 – 36 + 13

y = –5

Therefore, the vertex is (–3, –5).