Graph the square root functions and .

Question

Which function has a y-intercept?

(1 point)
Responses

f(x)
f of x

g(x)
g of x

both f(x) and g(x)
both f(x) and g(x)
Question 2
What are the coordinates of the minimum point for the square root function that relates to the quadratic function f(x)=−3(x−5)2+7


(2 points)
(
,
)

Answer 1

To assist you effectively, let's clarify the questions one by one:

Question 1: Graph the square root functions \( f(x) = \sqrt{x} \) and \( g(x) = \sqrt{x - 4} \).

1. Y-intercept:
   • The function \( f(x) = \sqrt{x} \) has a y-intercept at the point where \( x = 0 \).
     • When \( x = 0: f(0) = \sqrt{0} = 0 \) → The y-intercept is (0, 0).
   • The function \( g(x) = \sqrt{x - 4} \) does not have a y-intercept because it is undefined for \( x < 4 \).
     • The smallest value \( x \) can take is 4, where \( g(4) = \sqrt{4 - 4} = \sqrt{0} = 0 \).

Therefore, only \( f(x) \) has a y-intercept.

Answer: f(x)

Question 2: Minimum point for the quadratic function \( f(x) = -3(x - 5)^2 + 7 \).

This is a quadratic function in vertex form, where the vertex (minimum or maximum point) can be identified as follows:

In the vertex form \( f(x) = a(x - h)^2 + k \):

• The vertex is at the point \( (h, k) \).
• Here, \( a = -3 \), \( h = 5 \), and \( k = 7 \).

Since \( a < 0 \), the vertex is a maximum point.

Thus, the coordinates of the vertex (maximum point) of the quadratic function are:

Answer: (5, 7)

Summary:

• Question 1: \( f(x) \) has a y-intercept.
• Question 2: The minimum point for the quadratic function is \( (5, 7) \).