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) About Me  (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 x=-+%28b%2F%282%2Aa%29%29. This represents the X coordinate of your axis of symmetry. Note that your formula is in standard quadratic form y=%28a%2Ax%5E2%2Bb%2Ax%2Bc%29. Let's do the necessary substitutions and perform the necessary operations.
x=-%28%28-18%29%2F%282%2A3%29%29 We are substituting -18 for b and 3 for a.
x=-%28%28-18%29%2F%286%29%29 Simplification step 1 Multiplying 2 times 3
x=-%28%28-3%29%29 Simplification step 2 Dividing -18 by 6
x=3 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.
y=%283%2A3%5E2-18%2A3%2B32%29 Each x in the original equation has been replaced
with 3.
Now to solve the equation y=%283%2A3%5E2-18%2A3%2B32%29
A. Simplify the exponents y=%283%2A9-18%2A3%2B32%29
B. Simplify any multiplication y=%2827-54%2B32%29
C. Perform addition/subtraction y=%2827-54%2B32%29 = 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.
graph%28300%2C+200%2C+-6%2C+6%2C+-10%2C+10%2C+3%2Ax%5E2-18%2Ax%2B32%29