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

y=x^(2)-8x-2
Vertex Form:
y=
Vertex:
(◻,◻)

Put the quadratic into vertex form and state the coordinates of the vertex. $\newline$ $y=x^{2}-8 x-2$ $\newline$ 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}-8 x-2

\newline

Vertex Form:

y=

\newline

Vertex:

(\square, \square)

Identify Vertex Form: Identify the vertex form of a parabola. $\newline$ Vertex form: $y = a(x - h)^2 + k$
Complete the Square: Consider the given quadratic equation $y = x^2 - 8x - 2$ . $\newline$ To complete the square, we need to find a value that, when added and subtracted to the equation, forms a perfect square trinomial.
Calculate Half Coefficient Square: Calculate the square of half the coefficient of the $x$ term to complete the square. $\newline$ Half of the coefficient of $x$ is $-\frac{8}{2} = -4$ . $\newline$ Squaring this value gives $(-4)^2 = 16$ .
Form Perfect Square Trinomial: Add and subtract the calculated value inside the equation to form a perfect square trinomial. $\newline$ $y = x^2 - 8x + 16 - 16 - 2$ $\newline$ $y = (x^2 - 8x + 16) - 18$
Rewrite Equation with Trinomial: Rewrite the equation with the perfect square trinomial and the constant term. $\newline$ $y = (x - 4)^2 - 18$ $\newline$ This is the vertex form of the quadratic equation.
Identify Vertex Coordinates: Identify the vertex coordinates from the vertex form. $\newline$ The vertex form $y = a(x - h)^2 + k$ gives the vertex coordinates as $(h, k)$ . $\newline$ From $y = (x - 4)^2 - 18$ , the vertex coordinates are $(4, -18)$ .

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What is the focus of the parabola

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Simplify any fractions.

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In which direction does the parabola

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\newline

\newline

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\newline

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What is the axis of symmetry of the parabola

x = \frac{1}{2}(y + 3)^2 + 5

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Question

In which direction does the parabola

x - 2y^2 = -5

\newline

\newline

\text{[A]up}

\newline

\text{[B]down}

\newline

\text{[C]right}

\newline

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Question

What is the vertex of the parabola

y - 8x^2 = 4

\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

1

\newline

(B) The center is

(4,0)

and the radius is

1

\newline

(C) The center is

(0,4)

and the radius is

1

\newline

(D) The center is

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Posted 4 months ago

Question

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

\newline

The given equation is graphed in the

x y

-plane. Which of the following are

x

-intercepts of the graph?

\newline

1

\newline

-3

-9

\newline

-3

9

\newline

3

-9

\newline

3

9

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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

-coordinate of the vertex

\newline

y

-coordinate of the vertex

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