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).

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!

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virtuematane virtuematane · Answer 2 · 2019-06-07T11:10:11+02:00

Answer:

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

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

Step-by-step explanation:

The parent function f(x) is given by:

[tex]f(x)=x^2[/tex]

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 [tex]f(x)=0[/tex] we have:

[tex]x^2=0\\\\i.e.\\\\x=0[/tex]

Hence, x-intercept is:

(0,0) )

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

[tex]g(x)=-x^2-5[/tex]

Now, when [tex]g(x)=0[/tex] we have:

[tex]-x^2-5=0\\\\i.e.\\\\\\x^2=-5[/tex]

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

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