Answer:
Axis of symmetry: –3
Vertex: (–3, –5)
Step-by-step explanation:
For a quadratic function in standard form, the axis of symmetry is a vertical line [tex]x=-\frac{b}{2a}[/tex]. Therefore:
[tex]x=-\frac{b}{2a}=-\frac{12}{2(2)}=-\frac{12}{4}=-3[/tex]
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).
