The equation of a parabola is y = x^2 - 10x + 23. 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 the Square: Complete the square to rewrite the given equation in vertex form. We start with the given equation y = x^2 - 10x + 23. To complete the square, we need to find the value that makes x^2 - 10x a perfect square trinomial. We do this by taking half of the coefficient of x, which is -10, and squaring it. This gives us (-10/2)^2 = (-5)^2 = 25. We will add and subtract this value inside the equation.Add and Subtract Value: Add and subtract the value found in Step 2 to the equation. We add and subtract 25 to the equation, which gives us y = x^2 - 10x + 25 + 23 - 25. This allows us to form a perfect square trinomial without changing the value of the equation.Rewrite and Simplify: Rewrite the equation with the perfect square trinomial and simplify. Now we have y = (x^2 - 10x + 25) + 23 - 25. The expression in the parentheses is a perfect square trinomial, which can be factored as (x - 5)^2. Simplifying the constants gives us y = (x - 5)^2 - 2.

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The equation of a parabola is $y = x^2 - 10x + 23$ . Write the equation in vertex form. $\newline$ Write any numbers as integers or simplified proper or improper fractions. $\newline$ ______

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Algebra 1

Write a quadratic function in vertex form

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Q. The equation of a parabola is

y = x^2 - 10x + 23

. 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 the Square: Complete the square to rewrite the given equation in vertex form. $\newline$ We start with the given equation $y = x^2 - 10x + 23$ . To complete the square, we need to find the value that makes $x^2 - 10x$ a perfect square trinomial. We do this by taking half of the coefficient of $x$ , which is $-10$ , and squaring it. This gives us $(-10/2)^2 = (-5)^2 = 25$ . We will add and subtract this value inside the equation.
Add and Subtract Value: Add and subtract the value found in Step $2$ to the equation. $\newline$ We add and subtract $25$ to the equation, which gives us $y = x^2 - 10x + 25 + 23 - 25$ . This allows us to form a perfect square trinomial without changing the value of the equation.
Rewrite and Simplify: Rewrite the equation with the perfect square trinomial and simplify. $\newline$ Now we have $y = (x^2 - 10x + 25) + 23 - 25$ . The expression in the parentheses is a perfect square trinomial, which can be factored as $(x - 5)^2$ . Simplifying the constants gives us $y = (x - 5)^2 - 2$ .