Find the equation of the axis of symmetry for the parabola y = x^2 − 4x + 1 . Simplify any numbers and write them as proper fractions, improper fractions, or integers. _____

Identify coefficients: Identify the coefficients a and b from the quadratic equation y = ax^2 + bx + c. The given equation is y = x^2 − 4x + 1, which can be compared to the standard form y = ax^2 + bx + c. Here, a = 1 and b = -4.Calculate 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 = -(-4)/(2*1) x = 4/2 x = 2Write equation of axis: 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 = 2.

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Find the equation of the axis of symmetry for the parabola $y = x^2 - 4x + 1$ . $\newline$ 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 - 4x + 1

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

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Identify coefficients: Identify the coefficients $a$ and $b$ from the quadratic equation $y = ax^2 + bx + c$ . The given equation is $y = x^2 − 4x + 1$ , which can be compared to the standard form $y = ax^2 + bx + c$ . Here, $a = 1$ and $b = -4$ .
Calculate 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. $\newline$ $x = -\frac{-4}{2\cdot 1}$ $\newline$ $x = \frac{4}{2}$ $\newline$ $x = 2$
Write equation of axis: 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 $x = 2$ .