SOLUTION: Find the vertex and the axis of symmetry for the following graph:
{{{f(x)=3x^2-24x+51}}}
Algebra.Com
Question 131104: Find the vertex and the axis of symmetry for the following graph:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
To find the vertex, we first need to find the line of symmetry (ie the x-coordinate of the vertex)
To find the line of symmetry, use this formula:
From the equation we can see that a=3 and b=-24
Plug in b=-24 and a=3
Negate -24 to get 24
Multiply 2 and 3 to get 6
Reduce
So the line of symmetry is
So the x-coordinate of the vertex is . Lets plug this into the equation to find the y-coordinate of the vertex.
Lets evaluate
Start with the given polynomial
Plug in
Raise 4 to the second power to get 16
Multiply 3 by 16 to get 48
Multiply 24 by 4 to get 96
Now combine like terms
So the vertex is (4,3)
-----------------------
Answer:
So the line of symmetry is and the vertex is (4,3)
If we graph, we can visually verify our answer
Graph of with the line of symmetry and the vertex (4,3)
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