Question

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.

Answer 1

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

$y = a (x-h) ^ 2 + k$

Where the vertex coordinates are (h, k)

Comparing with the given equation:

 $f (x) = (x + 1) ^ 2 - 3$

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:

$f '(x) = 2 (x + 1)$

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

$2 (x + 1) = 0$

$x = -1$

Therefore the vertice of the parabola is:

$(h, k) = (-1, -3)$

And the axis of symmetry is:

$x = -1$

Answer:

Graphic 3

Answer 2

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