Put the quadratic into vertex form and state the coordinates of the vertex. y=x^(2)+2x+13 Vertex Form: y= Vertex: (◻,◻)

Identify Vertex Form: Identify the vertex form of a parabola. The vertex form of a parabola is y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.Complete Square: Complete the square to rewrite the quadratic equation in vertex form. Given equation: y = x^2 + 2x + 13 We need to find a value to add and subtract to complete the square. The coefficient of x is 2, so we take half of it, which is 1, and then square it to get 1. Add and subtract this value inside the parentheses: y = (x^2 + 2x + 1) - 1 + 13Simplify Equation: Simplify the equation by combining like terms. y = (x^2 + 2x + 1) + 12 Now, recognize that (x^2 + 2x + 1) is a perfect square trinomial. y = (x + 1)^2 + 12 This is the equation in vertex form.Identify Vertex: Identify the vertex of the parabola. From the vertex form y = (x + 1)^2 + 12, we can see that the vertex (h, k) is (-1, 12).

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Put the quadratic into vertex form and state the coordinates of the vertex.

y=x^(2)+2x+13
Vertex Form:
y=
Vertex:
(◻,◻)

Put the quadratic into vertex form and state the coordinates of the vertex. $\newline$ $y=x^{2}+2 x+13$ $\newline$ Vertex Form: $y=$ $\newline$ Vertex: $(\square, \square)$

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Algebra 2

Convert equations of parabolas from general to vertex form

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Q. Put the quadratic into vertex form and state the coordinates of the vertex.

\newline

y=x^{2}+2 x+13

\newline

Vertex Form:

y=

\newline

Vertex:

(\square, \square)

Identify Vertex Form: Identify the vertex form of a parabola. $\newline$ The vertex form of a parabola is $y = a(x - h)^2 + k$ , where $(h, k)$ is the vertex of the parabola.
Complete Square: Complete the square to rewrite the quadratic equation in vertex form. $\newline$ Given equation: $y = x^2 + 2x + 13$ $\newline$ We need to find a value to add and subtract to complete the square. $\newline$ The coefficient of $x$ is $2$ , so we take half of it, which is $1$ , and then square it to get $1$ . $\newline$ Add and subtract this value inside the parentheses: $y = (x^2 + 2x + 1) - 1 + 13$
Simplify Equation: Simplify the equation by combining like terms. $\newline$ $y = (x^2 + 2x + 1) + 12$ $\newline$ Now, recognize that $(x^2 + 2x + 1)$ is a perfect square trinomial. $\newline$ $y = (x + 1)^2 + 12$ $\newline$ This is the equation in vertex form.
Identify Vertex: Identify the vertex of the parabola. $\newline$ From the vertex form $y = (x + 1)^2 + 12$ , we can see that the vertex $(h, k)$ is $(-1, 12)$ .