Final answer:
To find the vertex of a quadratic equation, use x=-b/2a. For the given equation, the vertex is (-3,4). The axis of symmetry is x=-3. The x-intercepts are x=-1 and x=-5. The y-intercept is (0,5).
Step-by-step explanation:
The quadratic equation y=x²+6x+5 can be used to find the vertex, axis of symmetry, and intercepts. The vertex of a quadratic equation in the form y=ax²+bx+c can be found using the formula x=-b/2a. In this case, a=1, b=6, and c=5, so the x-coordinate of the vertex is -6/2(1)=-3. To find the y-coordinate, substitute the x-coordinate into the equation. Therefore, y=(-3)²+6(-3)+5=4. So, the vertex is (-3,4). The axis of symmetry is the line that passes through the vertex and is parallel to the y-axis. In this case, the equation of the axis of symmetry is x=-3. To find the intercepts, set y to 0 and solve for x. For the x-intercepts, y=0, so x²+6x+5=0. This can be factored as (x+1)(x+5)=0. So, the x-intercepts are x=-1 and x=-5. For the y-intercept, set x to 0, so y=(0)²+6(0)+5=5. Therefore, the y-intercept is (0,5).