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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

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

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

(−1,−5)

1 answer

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

  1. For the point \((-1, -3)\): \[ y = (2(-1) + 1)^2 - 4 = (-2 + 1)^2 - 4 = (-1)^2 - 4 = 1 - 4 = -3 \] So, \((-1, -3)\) is on the graph.

  2. For the point \((1, 2)\): \[ y = (2(1) + 1)^2 - 4 = (2 + 1)^2 - 4 = 3^2 - 4 = 9 - 4 = 5 \] So, \((1, 2)\) is NOT on the graph.

  3. For the point \((0, -2)\): \[ y = (2(0) + 1)^2 - 4 = (0 + 1)^2 - 4 = 1^2 - 4 = 1 - 4 = -3 \] So, \((0, -2)\) is NOT on the graph.

  4. For the point \((-1, -5)\): \[ y = (2(-1) + 1)^2 - 4 = (-2 + 1)^2 - 4 = (-1)^2 - 4 = 1 - 4 = -3 \] So, \((-1, -5)\) is NOT on the graph.

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