Find the equation of the axis of symmetry for the parabola y = x^2 − 2x + 29/4 . Simplify any numbers and write them as proper fractions, improper fractions, or integers. _____

Identify values of quadratic equation: Identify the values of a, b, and c in the quadratic equation y = ax^2 + bx + c. The given equation is y = x^2 - 2x + 29/4. Comparing this with the standard form, we get: a = 1 b = -2 c = 29/4Find axis of symmetry: Use the formula for the axis of symmetry, which is x = -b/(2a), to find the axis of symmetry for the parabola. Substitute the values of a and b into the formula: x = -(-2)/(2 × 1) x = 2/2 x = 1Write equation of symmetry: Write the equation of the axis of symmetry. The axis of symmetry is a vertical line, so its equation is of the form x = constant. Therefore, the equation of the axis of symmetry for the given parabola is x = 1.

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Find the equation of the axis of symmetry for the parabola $y = x^2 - 2x + \frac{29}{4}$ . $\newline$ 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 - 2x + \frac{29}{4}

\newline

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

\newline

_____

Identify values of quadratic equation: Identify the values of $a$ , $b$ , and $c$ in the quadratic equation $y = ax^2 + bx + c$ . The given equation is $y = x^2 - 2x + \frac{29}{4}$ . Comparing this with the standard form, we get: $a = 1$ $b = -2$ $c = \frac{29}{4}$
Find axis of symmetry: Use the formula for the axis of symmetry, which is $x = -\frac{b}{2a}$ , to find the axis of symmetry for the parabola. $\newline$ Substitute the values of $a$ and $b$ into the formula: $\newline$ $x = -\frac{-2}{2 \times 1}$ $\newline$ $x = \frac{2}{2}$ $\newline$ $x = 1$
Write equation of symmetry: Write the equation of the axis of symmetry. $\newline$ The axis of symmetry is a vertical line, so its equation is of the form $x = \text{constant}$ . $\newline$ Therefore, the equation of the axis of symmetry for the given parabola is $x = 1$ .