The equation of a parabola is y = x^2 – 10x + 25. Write the equation in vertex form. Write any numbers as integers or simplified proper or improper fractions. ______

Identify vertex form: Identify the vertex form of a parabola. The vertex form of a parabola is given by the equation y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.Complete square: Complete the square to rewrite the given equation in vertex form. The given equation is y = x^2 - 10x + 25. To complete the square, we need to express the quadratic term and the linear term as a perfect square trinomial.Find square of half: Find the square of half the coefficient of x. The coefficient of x is -10. Half of this coefficient is -10/2, which is -5. Squaring -5 gives us 25.Write as perfect square trinomial: Write the equation as a perfect square trinomial. Since the constant term 25 is already the square of -5, we can write the equation as y = (x - 5)^2. This is because x^2 - 10x + 25 is equivalent to (x - 5)^2.Write final equation in vertex form: Write the final equation in vertex form. The equation y = (x - 5)^2 is already in vertex form, with the vertex being (5, 0).

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The equation of a parabola is $y = x^2 - 10x + 25$ . Write the equation in vertex form. $\newline$ Write any numbers as integers or simplified proper or improper fractions. $\newline$ ______

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Algebra 2

Convert equations of parabolas from general to vertex form

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Q. The equation of a parabola is

y = x^2 - 10x + 25

. Write the equation in vertex form.

\newline

Write any numbers as integers or simplified proper or improper fractions.

\newline

______

Identify vertex form: Identify the vertex form of a parabola. $\newline$ The vertex form of a parabola is given by the equation $y = a(x - h)^2 + k$ , where $(h, k)$ is the vertex of the parabola.
Complete square: Complete the square to rewrite the given equation in vertex form. $\newline$ The given equation is $y = x^2 - 10x + 25$ . To complete the square, we need to express the quadratic term and the linear term as a perfect square trinomial.
Find square of half: Find the square of half the coefficient of $x$ . $\newline$ The coefficient of $x$ is $-10$ . Half of this coefficient is $-10/2$ , which is $-5$ . Squaring $-5$ gives us $25$ .
Write as perfect square trinomial: Write the equation as a perfect square trinomial. $\newline$ Since the constant term $25$ is already the square of $-5$ , we can write the equation as $y = (x - 5)^2$ . This is because $x^2 - 10x + 25$ is equivalent to $(x - 5)^2$ .
Write final equation in vertex form: Write the final equation in vertex form. $\newline$ The equation $y = (x - 5)^2$ is already in vertex form, with the vertex being $(5, 0)$ .