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Sanjay begins to correctly graph the function f(x) = (x + 1)2 – 3. Based on the axis of symmetry and the vertex, which graph could be Sanjay’s?
A.

Sanjay begins to correctly graph the function fx x 12 3 Based on the axis of symmetry and the vertex which graph could be Sanjays A class=
Sanjay begins to correctly graph the function fx x 12 3 Based on the axis of symmetry and the vertex which graph could be Sanjays A class=
Sanjay begins to correctly graph the function fx x 12 3 Based on the axis of symmetry and the vertex which graph could be Sanjays A class=
Sanjay begins to correctly graph the function fx x 12 3 Based on the axis of symmetry and the vertex which graph could be Sanjays A class=

Respuesta :

carlosego

For this case, the generic equation of a vertex shaped parabola is given by:

[tex]y = a (x-h) ^ 2 + k\\[/tex]

Where the vertex coordinates are (h, k)

Comparing with the given equation:

 [tex]f (x) = (x + 1) ^ 2 - 3\\[/tex]

It is observed that h = -1 and k = -3 to obtain the form of the generic equation.

To find the axis of symmetry we derive the given function:

[tex]f '(x) = 2 (x + 1)\\[/tex]

We equate this derivative to zero and clear the value of x

[tex]2 (x + 1) = 0\\[/tex]

[tex]x = -1\\[/tex]

Therefore the vertice of the parabola is:

[tex](h, k) = (-1, -3)\\[/tex]

And the axis of symmetry is:

[tex]x = -1\\[/tex]

Answer:

Graphic 3

The graph third represents the vertex and axis of symmetry of the function f(x) = (x + 1)² - 3 option third is correct.

What is a quadratic function?

Any function of the form [tex]\rm f(x) =ax^2+bx+c[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic function.

We have a function:

f(x) = (x + 1)² - 3

The above function is a quadratic function or parabolic function.

The vertex form of the function:

f(x) = (x - h)² + k

On comparing:

h = -1, k =  -3

(h, k) = (-1, -3) is the vertex of the function.

Axis of symmetery:

x + 1 = 0

x = -1

Thus, the graph third represents the vertex and axis of symmetry of the function f(x) = (x + 1)² - 3 option third is correct.

Learn more about quadratic function here:

brainly.com/question/2263981

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