Question

A function is in the form g(x) = x2 + d. If d < 0, which could be the graph of g(x)?

Answer 1

Please refer to the attached image for a possible graph of given equation.

Explanation:

Given the equation:

`g(x) = x^2 + d`

Let us write the equation as:

`y = x^2 + d` so that we can plot it on xy axis.

The highest power of x is 2.

The given equation resembles with the equation of a parabola.

The vertex form of a parabola is given as:

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

Here (h,k) is the vertex of parabola.

Vertex of the parabola is the point on the axis of symmetry and is the highest or the lowest point on parabola.

Now, let us compare the given equation of parabola with the standard vertex form of parabola. We get the following values:

a = 1 > 0 hence, parabola will open upwards.

h = 0

k = d

So, the vertex is at O (0,d). It means vertex will be on the y axis.

Now, we are given that d < 0 that means the vertex will be on negative y axis.

Now, let us suppose d = -8, the graph will be as attached in the answer area. Please have a look.