SOLUTION: I need to find the vertex of the parabola f(x)=-x2+3x-1

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Question 126178: I need to find the vertex of the parabola
f(x)=-x2+3x-1
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%283%29%2F%282%2A1%29%29 We are substituting 3 for b and 1 for a.
x=-%28%283%29%2F%282%29%29 Simplification step 1 Multiplying 2 times 1
x=-%28%283%29%2F2%29%29 Simplification step 2 Dividing 3 by 2
x=-3%2F2 Simplification step 3 -1 times 3/2.
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 or -1 1/2.
2. We now can substitute -3/2 into our original quadratic formula to solve for y.
y=%28%28-3%2F2%29%5E2%2B3%2A%28-3%2F2%29-1%29 Each x in the original equation has been replaced with -3/2

Now to solve the equation y=%28-3%2F2%29%5E2%2B3%2A%28-3%2F2%29-1%29
A. Simplify the exponents Y=%289%2F4%29%2B3%2A%28-3%2F2%29-1
This involves multiplying fractions.
%28-3%2F2%29%2A%28-3%2F2%29=%289%2F4%29
B. Simplify any multiplication Y=%289%2F4%29%2B3%2A%28-3%2F2%29-1
Again this involves multiplying whole numbers and fractions.
%283%2F1%29%2A%28-3%2F2%29=%28-9%2F2%29

C. Perform addition/subtraction y=%289%2F4%29-%289%2F2%29-1%29
This involves converting whole numbers to fractions and adding or
or subtracting, as the case may be.
%289%2F4%29-%289%2F2%29-%281%2F1%29=%289%2F4%29-%2818%2F4%29-%284%2F4%29=%28-15%2F4%29OR-3++3%2F4

The Y coordinate of our axis of symmetry and vertex is -3 3/4.

3. Therefore the vertex of the parabola is (-3/2,-3 3/4).
If you would rather work in decimal form, convert each fraction to a decimal.
%28-3%2F2%29=-1.50 and %28-15%2F4%29=-3.75
See the graph below.
graph%28300%2C+200%2C+-6%2C+6%2C+-10%2C+10%2C+x%5E2%2B3%2Ax-1%29