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

y=x^(2)-10 x+50
Vertex Form:
y=
Vertex:
(◻,◻)

Put the quadratic into vertex form and state the coordinates of the vertex. $\newline$ $y=x^{2}-10 x+50$ $\newline$ 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}-10 x+50

\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: $y = x^2 - 10x + 50$ $\newline$ To complete the square, we need to find a value that makes $x^2 - 10x$ a perfect square trinomial. $\newline$ The value to add and subtract is $(\frac{10}{2})^2 = 5^2 = 25$ .
Add and Subtract Value: Add and subtract the value found in Step $2$ inside the equation. $\newline$ $y = x^2 - 10x + 25 + 50 - 25$ $\newline$ $y = (x^2 - 10x + 25) + 25$ $\newline$ Now, the equation $x^2 - 10x + 25$ is a perfect square trinomial.
Factor and Simplify: Factor the perfect square trinomial and simplify the equation. $\newline$ $y = (x - 5)^2 + 25$ $\newline$ This is the equation in vertex form.
Identify Parabola Vertex: Identify the vertex of the parabola. $\newline$ The vertex form of the equation is $y = (x - h)^2 + k$ . $\newline$ Comparing this with the equation from Step $4$ , we get $h = 5$ and $k = 25$ . $\newline$ Therefore, the vertex of the parabola is $(5, 25)$ .

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