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Quadratic Functions

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

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Kyle R. | Mathematics and Science Tutor - Graduate StudentMathematics and Science Tutor - Graduate...
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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).