Graph of a Function Quick Check

Question

1 of 51 of 5 Items
Question
Which of the following is a point on the graph as described by the function y=(2x+1)2−4
?(1 point)
Responses

(1,2)
left parenthesis 1 comma 2 right parenthesis

(−1,−3)
left parenthesis negative 1 comma negative 3 right parenthesis

(0,−2)
left parenthesis 0 comma negative 2 right parenthesis

(−1,−5)

Answer 1

To determine which point is on the graph of the function \( y = (2x + 1)^2 - 4 \), we will substitute each x-coordinate from the given points into the function and see if we get the corresponding y-coordinate.

1. For the point \( (1, 2) \): \[ y = (2(1) + 1)^2 - 4 = (2 + 1)^2 - 4 = 3^2 - 4 = 9 - 4 = 5 \] This gives us \( (1, 5) \), so it does not match \( (1, 2) \).

2. For the point \( (-1, -3) \): \[ y = (2(-1) + 1)^2 - 4 = (-2 + 1)^2 - 4 = (-1)^2 - 4 = 1 - 4 = -3 \] This gives us \( (-1, -3) \), so this point is a match.

3. For the point \( (0, -2) \): \[ y = (2(0) + 1)^2 - 4 = (0 + 1)^2 - 4 = 1^2 - 4 = 1 - 4 = -3 \] This gives us \( (0, -3) \), so it does not match \( (0, -2) \).

4. For the point \( (-1, -5) \): \[ y = (2(-1) + 1)^2 - 4 = (-2 + 1)^2 - 4 = (-1)^2 - 4 = 1 - 4 = -3 \] This gives us \( (-1, -3) \), so it does not match \( (-1, -5) \).

The point that is on the graph of the function \( y = (2x + 1)^2 - 4 \) is \( \boxed{(-1, -3)} \).