Find the equation of the axis of symmetry for the parabola y = x^2 + x + 2 . Simplify any numbers and write them as proper fractions, improper fractions, or integers. _____

Identify Quadratic Equation: The general form of a quadratic equation is y = ax^2 + bx + c. To find the axis of symmetry, we use the formula x = -b/(2a). For the given parabola y = x^2 + x + 2, we can identify a = 1 and b = 1 by comparing it to the general form.Calculate Axis of Symmetry: Now we substitute the values of a and b into the formula for the axis of symmetry. x = -b/(2a) = -1/(2*1) = -1/2Equation of Axis of Symmetry: The equation of the axis of symmetry is therefore x = -1/2. This is a vertical line that passes through the point (-1/2, y) for all values of y.

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Find the equation of the axis of symmetry for the parabola $y = x^2 + x + 2$ . $\newline$ Simplify any numbers and write them as proper fractions, improper fractions, or integers. $\newline$ $\_\_\_\_\_$

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Algebra 2

Characteristics of quadratic functions: equations

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Q. Find the equation of the axis of symmetry for the parabola

y = x^2 + x + 2

\newline

Simplify any numbers and write them as proper fractions, improper fractions, or integers.

\newline

\_\_\_\_\_

Identify Quadratic Equation: The general form of a quadratic equation is $y = ax^2 + bx + c$ . To find the axis of symmetry, we use the formula $x = -\frac{b}{2a}$ . $\newline$ For the given parabola $y = x^2 + x + 2$ , we can identify $a = 1$ and $b = 1$ by comparing it to the general form.
Calculate Axis of Symmetry: Now we substitute the values of $a$ and $b$ into the formula for the axis of symmetry. $x = -\frac{b}{2a} = -\frac{1}{2\cdot 1} = -\frac{1}{2}$
Equation of Axis of Symmetry: The equation of the axis of symmetry is therefore $x = -\frac{1}{2}$ . This is a vertical line that passes through the point $(-\frac{1}{2}, y)$ for all values of $y$ .