Answer :
To find the axis of symmetry for the given parabola [tex]\( y = -x^2 - 2x + 6 \)[/tex], you can follow these steps:
1. Identify the coefficients of the quadratic equation: The given quadratic equation can be written in standard form [tex]\( y = ax^2 + bx + c \)[/tex], which makes it clear that:
- [tex]\( a = -1 \)[/tex]
- [tex]\( b = -2 \)[/tex]
- [tex]\( c = 6 \)[/tex]
2. Use the formula for the axis of symmetry: For a parabola given by [tex]\( y = ax^2 + bx + c \)[/tex], the axis of symmetry is given by the formula [tex]\( x = -\frac{b}{2a} \)[/tex].
3. Substitute the values of [tex]\( a \)[/tex] and [tex]\( b \)[/tex] into the formula:
- [tex]\( a = -1 \)[/tex]
- [tex]\( b = -2 \)[/tex]
The formula becomes:
[tex]\[ x = -\frac{-2}{2 \cdot -1} \][/tex]
4. Simplify the expression: Calculate the value inside the fraction.
[tex]\[ x = -\frac{-2}{-2} \][/tex]
5. Calculate the final value:
[tex]\[ x = -1 \][/tex]
Therefore, the axis of symmetry for the parabola [tex]\( y = -x^2 - 2x + 6 \)[/tex] is given by the equation:
[tex]\[ x = -1 \][/tex]
1. Identify the coefficients of the quadratic equation: The given quadratic equation can be written in standard form [tex]\( y = ax^2 + bx + c \)[/tex], which makes it clear that:
- [tex]\( a = -1 \)[/tex]
- [tex]\( b = -2 \)[/tex]
- [tex]\( c = 6 \)[/tex]
2. Use the formula for the axis of symmetry: For a parabola given by [tex]\( y = ax^2 + bx + c \)[/tex], the axis of symmetry is given by the formula [tex]\( x = -\frac{b}{2a} \)[/tex].
3. Substitute the values of [tex]\( a \)[/tex] and [tex]\( b \)[/tex] into the formula:
- [tex]\( a = -1 \)[/tex]
- [tex]\( b = -2 \)[/tex]
The formula becomes:
[tex]\[ x = -\frac{-2}{2 \cdot -1} \][/tex]
4. Simplify the expression: Calculate the value inside the fraction.
[tex]\[ x = -\frac{-2}{-2} \][/tex]
5. Calculate the final value:
[tex]\[ x = -1 \][/tex]
Therefore, the axis of symmetry for the parabola [tex]\( y = -x^2 - 2x + 6 \)[/tex] is given by the equation:
[tex]\[ x = -1 \][/tex]
