Question

The functiong(x)is graphed below.

The graph of which function has the same vertex asg(x)?
1Choice 1
q(x)=x2−5
2Choice 2
h(x)=(x−3)2+4
3Choice 3
p(x)=(x+3)2+4
4Choice 4
f(x)=(x−5)2+1

Answer 1

Step-by-step explanation:

I say

4choice4

Answer 2

This function has the same vertex as g(x) is Choice 2:
`h(x) = (x - 3)^2 + 4`

The answer is option ⇒2

Step-by-step explanation:

The graph of the function g(x) is given, and we are asked to identify which function has the same vertex as g(x).

To find the vertex of a quadratic function in the form
`f(x) = a(x - h)^2 + k`, where (h, k) represents the vertex, we can compare the given function g(x) with the options provided.

Let's analyze each choice:

1.
`q(x) = x^2 - 5`: This function does not match the form of g(x) since it has a different constant term (-5 instead of 0). Therefore, it does not have the same vertex as g(x).

2.
`h(x) = (x - 3)^2 + 4`: This function matches the form of g(x) (a perfect square trinomial with no constant term). Both g(x) and h(x) have the same vertex at (3, 4).

3.
`p(x) = (x + 3)^2 + 4`: This function does not match the form of g(x) since it has a different constant term (4 instead of 0). Therefore, it does not have the same vertex as g(x).

4.
`f(x) = (x - 5)^2 + 1`: This function does not match the form of g(x) since it has a different constant term (1 instead of 0). Therefore, it does not have the same vertex as g(x).

Therefore, the correct answer is Choice 2:
`h(x) = (x - 3)^2 + 4`. This function has the same vertex as g(x).

The answer is option ⇒2