SOLUTION: I need to find the vertex of the parabola f(x)=3x2-18x+32

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Question 126176: I need to find the vertex of the parabola
f(x)=3x2-18x+32

Answer by JessicaGill(40)   (Show Source): You can put this solution on YOUR website!
To determine the vertex of a parabola without actually graphing it, you can use the following steps to obtain it.
1. First use the formula . This represents the X coordinate of your axis of symmetry. Note that your formula is in standard quadratic form . Let's do the necessary substitutions and perform the necessary operations.
We are substituting -18 for b and 3 for a.
Simplification step 1 Multiplying 2 times 3
Simplification step 2 Dividing -18 by 6
Simplification step 4 -1 times -3.
The negative 1 (-1) comes from the negative of
the entire formula. See step 1 for the
formula description.
Our x coordinate for the vertex and axis of symmetry is 3.
2. We now can substitute 3 into our original quadratic formula to solve for y.
Each x in the original equation has been replaced
with 3.
Now to solve the equation
A. Simplify the exponents
B. Simplify any multiplication
C. Perform addition/subtraction = 5
The Y coordinate of our axis of symmetry and vertex is 5.
3. Therefore the vertex of the parabola is (3,5) See the graph below.



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