The equation of a parabola is y = x^2 - 8x + 18. 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 y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.Consider given equation: Consider the given equation y = x^2 - 8x + 18. We need to complete the square to rewrite this equation in vertex form.Find square of half: Find the square of half the coefficient of x. Half the coefficient of x is -8/2, which is -4. Squaring this gives us (-4)^2 = 16.Add and subtract square: Add and subtract the square of half the coefficient of x inside the equation. y = x^2 - 8x + 16 - 16 + 18 We add and subtract 16 to complete the square while keeping the equation balanced.Rewrite equation by grouping: Rewrite the equation by grouping the perfect square trinomial and combining the constants. y = (x^2 - 8x + 16) - 16 + 18 y = (x - 4)^2 + 2 Now the equation is in vertex form, where (h, k) = (4, 2).

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The equation of a parabola is $y = x^2 - 8x + 18$ . 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 - 8x + 18

. 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 $y = a(x - h)^2 + k$ , where $(h, k)$ is the vertex of the parabola.
Consider given equation: Consider the given equation $y = x^2 - 8x + 18$ . $\newline$ We need to complete the square to rewrite this equation in vertex form.
Find square of half: Find the square of half the coefficient of $x$ . Half the coefficient of $x$ is $-8/2$ , which is $-4$ . Squaring this gives us $(-4)^2 = 16$ .
Add and subtract square: Add and subtract the square of half the coefficient of $x$ inside the equation. $\newline$ $y = x^2 - 8x + 16 - 16 + 18$ $\newline$ We add and subtract $16$ to complete the square while keeping the equation balanced.
Rewrite equation by grouping: Rewrite the equation by grouping the perfect square trinomial and combining the constants. $\newline$ $y = (x^2 - 8x + 16) - 16 + 18$ $\newline$ $y = (x - 4)^2 + 2$ $\newline$ Now the equation is in vertex form, where $(h, k) = (4, 2)$ .