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

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

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

(−1,−5)
left parenthesis negative 1 comma negative 5 right parenthesis
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Answer 1

To determine which of the given points is on the graph of the function \( y = (2x + 1)^2 - 4 \), we can evaluate the function at each specified \( x \)-value and see if it matches the corresponding \( y \)-value.

1. For \( (-1, -3) \): \[ y = (2(-1) + 1)^2 - 4 = (-2 + 1)^2 - 4 = (-1)^2 - 4 = 1 - 4 = -3 \] This point is valid.

2. For \( (0, -2) \): \[ y = (2(0) + 1)^2 - 4 = (0 + 1)^2 - 4 = 1 - 4 = -3 \] This does not match \( -2 \).

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

4. For \( (-1, -5) \): \[ y = (2(-1) + 1)^2 - 4 = (-2 + 1)^2 - 4 = (-1)^2 - 4 = 1 - 4 = -3 \] This does not match \( -5 \).

Therefore, the only point that is on the graph of the function is: (−1,−3)