SOLUTION: What is the vertex and equation of symmetry of F(x)= 2x^2+6x+8

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Question 1138648: What is the vertex and equation of symmetry of F(x)= 2x^2+6x+8
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

the vertex and equation of symmetry of F%28x%29=+2x%5E2%2B6x%2B8
to find the vertex write equation in the vertex form:f%28x%29=a%28x-h%29%5E2%2Bk where h and k are x and f%28x%29 coordinates of the vertex
F%28x%29=+%282x%5E2%2B6x%29%2B8.......group and complete square
F%28x%29=+2%28x%5E2%2B3x%29%2B8

F%28x%29=+2%28x%5E2%2B3x%2Bb%5E2%29-2b%5E2%2B8.......b=3%2F2->(recall b is equal to half of the coefficient of variable x%5E1)
F%28x%29=+2%28x%5E2%2B3x%2B%283%2F2%29%5E2%29-2%283%2F2%29%5E2%2B8
F%28x%29=+2%28x%2B3%2F2%29%5E2-2%289%2F4%29%2B8

F%28x%29=+2%28x%2B3%2F2%29%5E2-9%2F2%2B8
F%28x%29=+2%28x%2B3%2F2%29%5E2-9%2F2%2B16%2F2
F%28x%29=+2%28x%2B3%2F2%29%5E2%2B7%2F2
=>h=-3%2F2 and k=7%2F2; so, vertex is at (-3%2F2,7%2F2)

Axis of Symmetry for y=ax%5E2%2Bbx%2Bc is : x=+-b%2F2a+
which is vertical line that passes through x coordinate of the vertex; in your case, axis of symmetry is x=-3%2F2