To determine the axis of symmetry for the quadratic function [tex]\( v = 2x^2 - 4x + 2 \)[/tex], follow these steps:
1. Identify the coefficients: In the general form of a quadratic equation [tex]\( ax^2 + bx + c \)[/tex], identify the coefficients [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex].
For the given equation [tex]\( v = 2x^2 - 4x + 2 \)[/tex]:
- [tex]\( a = 2 \)[/tex]
- [tex]\( b = -4 \)[/tex]
- [tex]\( c = 2 \)[/tex]
2. Use the formula for the axis of symmetry: The axis of symmetry for a quadratic equation of the form [tex]\( ax^2 + bx + c \)[/tex] is calculated using the formula:
[tex]\[
x = -\frac{b}{2a}
\][/tex]
3. Substitute the coefficients into the formula:
- Plug [tex]\( a = 2 \)[/tex] and [tex]\( b = -4 \)[/tex] into the formula:
[tex]\[
x = -\frac{-4}{2 \times 2}
\][/tex]
4. Simplify the expression:
- Calculate the denominator: [tex]\( 2 \times 2 = 4 \)[/tex]
- Calculate the numerator: [tex]\( -(-4) = 4 \)[/tex]
- Divide the numerator by the denominator:
[tex]\[
x = \frac{4}{4} = 1
\][/tex]
Therefore, the axis of symmetry for the graph of [tex]\( v = 2x^2 - 4x + 2 \)[/tex] is:
[tex]\[
x = 1
\][/tex]
