The function f is given in three equivalent forms. Which form most quickly reveals the vertex? Choose 1 answer: (A) f(x)=-3(x-2)^(2)+27 (B) f(x)=-3(x+1)(x-5) (c) f(x)=-3x^(2)+12 x+15 What is the vertex? Vertex =(◻,◻)

Identify Vertex Form: Identify the form that reveals the vertex. The vertex form of a parabola is y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.Compare Given Forms: Compare the given forms of the function f. (A) f(x)=-3(x-2)^(2)+27 is already in vertex form. (B) f(x)=-3(x+1)(x-5) is in factored form, which does not directly reveal the vertex. (C) f(x)=-3x^(2)+12x+15 is in standard form, which also does not directly reveal the vertex.Determine Quickest Form: Determine which form most quickly reveals the vertex. Form (A) is already in vertex form, so it most quickly reveals the vertex of the parabola.Identify Vertex: Identify the vertex from form (A). In form (A), f(x)=-3(x-2)^(2)+27, we can see that h = 2 and k = 27. Therefore, the vertex is (2, 27).

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The function
f is given in three equivalent forms.
Which form most quickly reveals the vertex?
Choose 1 answer:
(A)
f(x)=-3(x-2)^(2)+27
(B)
f(x)=-3(x+1)(x-5)
(c)
f(x)=-3x^(2)+12 x+15
What is the vertex?
Vertex
=(◻,◻)

The function $\newline$ $f$ is given in three equivalent forms. $\newline$ Which form most quickly reveals the vertex? $\newline$ Choose $1$ answer: $\newline$ (A) $f(x)=-3(x-2)^{2}+27$ $\newline$ (B) $f(x)=-3(x+1)(x-5)$ $\newline$ (C) $f(x)=-3x^{2}+12x+15$ $\newline$ What is the vertex? $\newline$ Vertex $=(\square,\square)$

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Math Problems

Algebra 2

Convert equations of parabolas from general to vertex form

Full solution

Q. The function

\newline

f

is given in three equivalent forms.

\newline

Which form most quickly reveals the vertex?

\newline

Choose

1

answer:

\newline

(A)

f(x)=-3(x-2)^{2}+27

\newline

(B)

f(x)=-3(x+1)(x-5)

\newline

(C)

f(x)=-3x^{2}+12x+15

\newline

What is the vertex?

\newline

Vertex

=(\square,\square)

Identify Vertex Form: Identify the form that reveals the vertex. $\newline$ The vertex form of a parabola is $y = a(x - h)^2 + k$ , where $(h, k)$ is the vertex of the parabola.
Compare Given Forms: Compare the given forms of the function $f$ .
(A) $f(x)=-3(x-2)^{2}+27$ is already in vertex form.
(B) $f(x)=-3(x+1)(x-5)$ is in factored form, which does not directly reveal the vertex.
(C) $f(x)=-3x^{2}+12x+15$ is in standard form, which also does not directly reveal the vertex.
Determine Quickest Form: Determine which form most quickly reveals the vertex. $\newline$ Form (A) is already in vertex form, so it most quickly reveals the vertex of the parabola.
Identify Vertex: Identify the vertex from form (A). $\newline$ In form (A), $f(x)=-3(x-2)^{2}+27$ , we can see that $h = 2$ and $k = 27$ . $\newline$ Therefore, the vertex is $(2, 27)$ .