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

y=x^(2)+10 x+9
Vertex Form:
y=
Vertex:
(◻,◻)

Put the quadratic into vertex form and state the coordinates of the vertex. $\newline$ $y=x^{2}+10 x+9$ $\newline$ 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+9

\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 given by $y = a(x - h)^2 + k$ , where $(h, k)$ is the vertex of the parabola.
Given quadratic equation: Consider the given quadratic equation $y = x^2 + 10x + 9$ . $\newline$ To convert this into vertex form, we need to complete the square.
Factor out coefficient: Factor out the coefficient of the $x^2$ term if it is not $1$ . In this case, the coefficient is already $1$ , so we can proceed to the next step.
Find square of half: Find the square of half the coefficient of the $x$ term to complete the square. $\newline$ Half of the coefficient of $x$ is $\frac{10}{2} = 5$ . $\newline$ Squaring this gives us $5^2 = 25$ .
Add and subtract square: Add and subtract the square of half the coefficient of $x$ inside the equation. $\newline$ $y = x^2 + 10x + (5^2) - (5^2) + 9$ $\newline$ This step ensures that we can form a perfect square trinomial while keeping the equation balanced.
Rewrite equation grouping: Rewrite the equation grouping the perfect square trinomial and combining the constants. $\newline$ $y = (x^2 + 10x + 25) - 25 + 9$ $\newline$ $y = (x + 5)^2 - 16$
Equation in vertex form: Now the equation is in vertex form. $\newline$ Vertex Form: $y = (x + 5)^2 - 16$
Identify vertex coordinates: Identify the coordinates of the vertex from the vertex form. $\newline$ The vertex $(h, k)$ is given by the values inside the parenthesis and the constant term. $\newline$ Here, $h = -5$ and $k = -16$ . $\newline$ Vertex: $(-5, -16)$

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The given equation is graphed in the

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