# What is the axis of symmetry and vertex for the graph #y=3x^2+12x-2#?

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#### Explanation

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**Axis of Symmetry is the line **

**Vertex is at:** **It is a minimum.**

#### Explanation:

**Given:**

We use the **Quadratic formula** to find the **Solutions:**

Let us look at

We observe that

Substitute these values in our **Quadratic formula**:

We know that our **discriminant #b^2-4ac# ** is greater than zero.

Hence, **we have two real roots.**

Using a calculator, we can simplify and get the values:

Hence, our **x-intercepts are**:

To find the **Vertex**,

we can use the formula:

**Vertex:**

This is our **x-coordinate value of our Vertex.**

To find the **y-coordinate value of our Vertex:**

Substitute the value of

**Vertex is at:**

The coefficient of the **Positive** and hence, our **Parabola Opens Upward, and it has a minimum.** Please refer to the image of the graph below **to verify our solutions:**

The **Axis of symmetry of a parabola** is a **vertical line that divides the parabola into two congruent halves.**

The **Axis of Symmetry** always passes through the **Vertex** of the Parabola. The ** #x# coordinate of the vertex** is the equation of the Axis of Symmetry of the Parabola.

**Axis of Symmetry is the line **

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#### Explanation

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#### Answer:

Axis of symmetry:

Vertex:

#### Explanation:

This equation

To find the axis of symmetry, we do

We know that

So the axis of symmetry is

Now we want to find the vertex. The

To find the

So the vertex is

To visualize this, here is a graph of this equation:

Hope this helps!

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