Question

Find the axis of symmetry and the vertex of the graph of f(x)=x^2+8x+10

Answer 1

Axis of Symmetry: x = -4

Vertex: ( -4, -6 )

Explanation:

~ Part I ~

1. To find the axis of symmetry, rewrite y = x^2 + 8x + 10 in the parabola standard form ( 4p( y - k ) = ( x - h) ^2 for an up-down facing parabola at vertex ( h, k ) and a focal length |p|) ⇒ 4 * 1/4 ( y - ( - 6 ) ) = ( x - ( - 4 ) )^2

2. Therefore the parabola properties are ⇒ ( h, k ) = ( - 4, -6 ), p = 1/4

3. Answer: x = -4

~ Part II ~

1. From the previous question, we got that the vertex should be ⇒ ( -4, -6 )

2. Answer: ( -4, -6 )