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

y=x^(2)+4x+5
Vertex Form:
y=
Vertex:
(◻,◻)

Put the quadratic into vertex form and state the coordinates of the vertex. $\newline$ $y=x^{2}+4 x+5$ $\newline$ 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}+4 x+5

\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 transformation: Complete the square to transform the given quadratic equation into vertex form. $\newline$ The given quadratic equation is $y = x^2 + 4x + 5$ . $\newline$ To complete the square, we need to find a value that, when added and subtracted to the equation, forms a perfect square trinomial. $\newline$ The coefficient of $x$ is $4$ , so we take half of it, which is $2$ , and square it to get $4$ . $\newline$ We add and subtract this value inside the equation to complete the square.
Add/subtract squared value: Add and subtract the squared value inside the equation. $\newline$ $y = x^2 + 4x + 4 - 4 + 5$ $\newline$ Now, group the perfect square trinomial and the constants. $\newline$ $y = (x^2 + 4x + 4) - 4 + 5$
Factor perfect square trinomial: Factor the perfect square trinomial and simplify the constants. $\newline$ $y = (x + 2)^2 - 4 + 5$ $\newline$ $y = (x + 2)^2 + 1$ $\newline$ Now we have the equation in vertex form.
Identify parabola vertex: Identify the vertex of the parabola. $\newline$ The vertex form of the equation is $y = (x + 2)^2 + 1$ . $\newline$ Comparing this with the standard vertex form $y = a(x - h)^2 + k$ , we find that $h = -2$ and $k = 1$ . $\newline$ Therefore, the vertex of the parabola is $(-2, 1)$ .

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\newline

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Question

The equation of a circle is

x^{2}+(y+4)^{2}=1

. What are the center and radius of the circle?

\newline

1

\newline

(A) The center is

(-4,0)

and the radius is

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\newline

(B) The center is

(4,0)

and the radius is

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(D) The center is

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Question

y=(x-3)(x+9)

\newline

The given equation is graphed in the

x y

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x

-intercepts of the graph?

\newline

1

\newline

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9

\newline

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\newline

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Question

y=2 x^{2}-5 x+7

is graphed in the

x y

-plane, which of the following characteristics of the graph is displayed as a constant or coefficient in the equation?

\newline

1

\newline

x

\newline

y

\newline

x

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\newline

y

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