SOLUTION: Parabolas Determine the vertex of the given equation. y = 3x2

SOLUTION: Parabolas Determine the vertex of the given equation. y = 3x2 - 3x + 2

Question 453211: Parabolas
Determine the vertex of the given equation.
y = 3x2 - 3x + 2

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

In order to find the vertex, we first need to find the x-coordinate of the vertex.

To find the x-coordinate of the vertex, use this formula: .

Start with the given formula.

From , we can see that , , and .

Plug in and .

Negate to get .

Multiply 2 and to get .

Reduce.

So the x-coordinate of the vertex is . Note: this means that the axis of symmetry is also .

Now that we know the x-coordinate of the vertex, we can use it to find the y-coordinate of the vertex.

Start with the given equation.

Plug in .

Square to get .

Multiply and to get .

Multiply and to get .

Combine like terms.

So the y-coordinate of the vertex is .

So the vertex is

.

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