Quadratic Functions

Question

Find the vertex, equation of the axis of symmetry, and the y-y-intercept of y=x^2+4x+6

Answer 1

The equation for the axis of symmetry is x = -b/2a:

 

x = -4/2

x = -2

 

The axis of symmetry is x = -2.  

 

The axis of symmetry also gives you the x component of the vertex.  Plug in -2 for x to find the y component of the vertex:

 

y = x² + 4x + 6

y = (-2)² + 4(-2) + 6

y = 4 - 8 + 6

y = 4 - 2

y = 2

 

The vertex is (-2,2).

 

To find the y-intercept, plug in 0 for x and solve:

 

y = x² + 4x + 6

y = 0 + 0 + 6

y = 6

 

The y-intercept is (0,6).