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

Question

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

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

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

(0,−2)

Answer 1

To find the point on the graph as described by the function y=(2x+1)^2-4, we need to substitute the x-value into the equation and calculate the corresponding y-value.

Let's test each option:

For (−1,−3):
Substituting x=-1 into the equation:
y=(2(-1)+1)^2-4
y=(-2+1)^2-4
y=(-1)^2-4
y=1-4
y=-3

The calculated y-value does not match the given y-value of -3, so (-1,-3) is not a point on the graph as described by the function.

For (−1,−5):
Substituting x=-1 into the equation:
y=(2(-1)+1)^2-4
y=(-2+1)^2-4
y=(-1)^2-4
y=1-4
y=-3

The calculated y-value does not match the given y-value of -5, so (-1,-5) is not a point on the graph as described by the function.

For (1,2):
Substituting x=1 into the equation:
y=(2(1)+1)^2-4
y=(2+1)^2-4
y=3^2-4
y=9-4
y=5

The calculated y-value matches the given y-value of 2, so (1,2) is a point on the graph as described by the function.

For (0,−2):
Substituting x=0 into the equation:
y=(2(0)+1)^2-4
y=(0+1)^2-4
y=1^2-4
y=1-4
y=-3

The calculated y-value does not match the given y-value of -2, so (0,-2) is not a point on the graph as described by the function.

Therefore, the point on the graph as described by the function y=(2x+1)^2-4 is (1,2).