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

y=x^(2)-20 x+25
Vertex Form:
y=
Vertex:
(◻,◻)

Put the quadratic into vertex form and state the coordinates of the vertex. $\newline$ $y=x^{2}-20 x+25$ $\newline$ 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}-20 x+25

\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: $y = x^2 - 20x + 25$ $\newline$ To complete the square, we need to find the value that makes $x^2 - 20x$ a perfect square trinomial. $\newline$ We take half of the coefficient of $x$ , which is $-20$ , divide it by $2$ to get $-10$ , and then square it to get $100$ .
Add and subtract terms: Add and subtract the square of half the coefficient of $x$ inside the equation. $\newline$ We add and subtract $100$ inside the equation to maintain the equality. $\newline$ $y = x^2 - 20x + 100 - 100 + 25$
Group and combine: Group the perfect square trinomial and combine the constants. $\newline$ $y = (x^2 - 20x + 100) - 100 + 25$ $\newline$ $y = (x - 10)^2 - 75$ $\newline$ Now the equation is in vertex form.
Identify the vertex: Identify the vertex of the parabola. $\newline$ The vertex form of the equation is $y = (x - 10)^2 - 75$ . $\newline$ Comparing this with the standard vertex form $y = a(x - h)^2 + k$ , we find that $h = 10$ and $k = -75$ . $\newline$ Therefore, the vertex of the parabola is $(10, -75)$ .

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