Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

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 $=(\square,\square)$

View step-by-step help

View step-by-step help

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 $(2, 27)$ .

More problems from Convert equations of parabolas from general to vertex form

Question

What is the focus of the parabola

y = -x^2

\newline

Simplify any fractions.

\newline

(_____ , _____)

\newline

Posted 1 month ago

Question

The equation of a parabola is

y = x^2 - 10x + 25

. Write the equation in vertex form.

\newline

Write any numbers as integers or simplified proper or improper fractions.

\newline

Posted 2 months ago

Question

In which direction does the parabola

x + y^2 = -7

\newline

\newline

\text{up}

\newline

\text{down}

\newline

\text{right}

\newline

\text{left}

Posted 2 months ago

Question

What is the vertex of the parabola

y = -4(x - 2)^2 + 2

?

\newline

(\_,\_)

Posted 2 months ago

Question

What is the axis of symmetry of the parabola

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

Posted 2 months ago

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

\text{[D]left}

Posted 2 months ago

Question

What is the vertex of the parabola

y - 8x^2 = 4

\newline

(\_,\_)

Posted 1 month ago

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

(0,-4)

and the radius is

1

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

Posted 4 months ago

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

Posted 4 months ago