Question

In two or more complete sentences, compare the number of x-intercepts in the graph of f(x) = x2 to the number of x-intercepts in the graph of g(x) = -x2 -5. Be sure to include the transformations that occurred between the parent function f(x) and its image g(x).

Answer 1

Hi there!

A graph of the parabolas are show below.

There is one x intercept on the function f(x) = x^2 (the origin).
There are two x intercepts on the function g(x) = -x^2 - 5.

From the first function to the next, the function is flipped and the vertex is lowered by 5 on the y axis.

Hope this helps!

Answer 2

Graph of f(x) has: 1 x-intercept.

Graph of g(x) has: No x-intercept.

Explanation:

• The parent function f(x) is given by:

`f(x)=x^2`

We know that a x-intercept of a function is a point on the graph where the value of function is zero.

i.e. it is a point where the graph meets the x-axis.

Hence, from the graph of the function f(x) we see that the graph has one x-intercept.

( Since, when
`f(x)=0` we have:

`x^2=0\\\\i.e.\\\\x=0`

Hence, x-intercept is:

(0,0) )

• Now, the equation of the transformed function g(x) is given by:

`g(x)=-x^2-5`

Now, when
`g(x)=0` we have:

`-x^2-5=0\\\\i.e.\\\\\\x^2=-5`

which is not possible as square of a real quantity can't be negative.

Hence, the function g(x) has no x-intercept.