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

y=x^(2)-12 x-13
Vertex Form:
y=
Vertex:
(◻,◻)

Put the quadratic into vertex form and state the coordinates of the vertex. $\newline$ $y=x^{2}-12 x-13$ $\newline$ Vertex Form: $y=$ $\newline$ Vertex: $(\square, \square)$

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Convert equations of parabolas from general to vertex form

Full solution

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

\newline

y=x^{2}-12 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 the Square: Complete the square to rewrite the quadratic equation in vertex form. $\newline$ Given equation: $y = x^2 - 12x - 13$ $\newline$ To complete the square, we need to find a value that, when added and subtracted to the equation, forms a perfect square trinomial with the $x^2$ and $-12x$ terms. $\newline$ The value to complete the square is $(b/2)^2$ , where $b$ is the coefficient of the $x$ term. $\newline$ In this case, $b = -12$ , so $(b/2)^2 = (-12/2)^2 = (-6)^2 = 36$ .
Add Value Inside Equation: Add and subtract the value found in Step $2$ inside the equation. $\newline$ $y = x^2 - 12x + 36 - 36 - 13$ $\newline$ $y = (x^2 - 12x + 36) - 49$ $\newline$ Now, the equation includes the perfect square trinomial $(x^2 - 12x + 36)$ .
Factor and Simplify: Factor the perfect square trinomial and simplify the equation. $\newline$ $y = (x - 6)^2 - 49$ $\newline$ This is the vertex form of the quadratic equation.
Identify Parabola Vertex: Identify the vertex of the parabola from the vertex form. $\newline$ The vertex form is $y = a(x - h)^2 + k$ , so the vertex $(h, k)$ is $(6, -49)$ .

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