The equation of the axis of symmetry of the function `y=2x^(2)+3x-6` is

Options

A. `x=-(3)/(2)`
B. `x=-(3)/(4)`
C. `x=-(1)/(3)`
D. `x=(1)/(3)`

Explanation

To find the equation of the axis of symmetry for the quadratic function \( y = 2x^2 + 3x - 6 \), we can follow these steps:

### Step 1: Identify the coefficients
The standard form of a quadratic function is \( y = ax^2 + bx + c \). In our case:
- \( a = 2 \)
- \( b = 3 \)
- \( c = -6 \)

### Step 2: Use the formula for the axis of symmetry
The formula for the x-coordinate of the vertex (which is also the equation of the axis of symmetry) is given by:
\[ x = -\frac{b}{2a} \]

### Step 3: Substitute the values of \( a \) and \( b \)
Now, we substitute the values of \( a \) and \( b \) into the formula:
\[ x = -\frac{3}{2 \times 2} \]

### Step 4: Simplify the expression
Calculating the denominator:
\[ 2 \times 2 = 4 \]
Now substituting back into the equation:
\[ x = -\frac{3}{4} \]

### Step 5: Write the equation of the axis of symmetry
Thus, the equation of the axis of symmetry is:
\[ x = -\frac{3}{4} \]

### Final Answer:
The equation of the axis of symmetry of the function \( y = 2x^2 + 3x - 6 \) is \( x = -\frac{3}{4} \).

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