Which of the following is a point on the graph as described by the function y=(2x+1)2−4 ?(1 point) Responses (−1,−5) left parenthesis negative 1 comma negative 5 right parenthesis (0,−2) left parenthesis 0 comma negative 2 right parenthesis (1,2) left parenthesis 1 comma 2 right parenthesis (−1,−3)
To find the point on the graph, we substitute the x-coordinate into the function and calculate the corresponding y-coordinate.
Let's go through each option and see which one satisfies the equation:
1) For the point (-1,-5), substituting x = -1 into the function gives us:
y = (2(-1) + 1)^2 - 4
= ( -2 + 1 )^2 - 4
= (-1)^2 - 4
= 1 - 4
= -3
So, the y-coordinate is -3, not -5. This point does not lie on the graph.
2) For the point (0,-2), substituting x = 0 into the function gives us:
y = (2(0) + 1)^2 - 4
= (0 + 1)^2 - 4
= (1)^2 - 4
= 1 - 4
= -3
So, the y-coordinate is -3, not -2. This point does not lie on the graph.
3) For the point (1,2), substituting x = 1 into the function gives us:
y = (2(1) + 1)^2 - 4
= (2 + 1)^2 - 4
= (3)^2 - 4
= 9 - 4
= 5
So, the y-coordinate is 5. This point satisfies the equation and lies on the graph.
4) For the point (-1,-3), substituting x = -1 into the function gives us:
y = (2(-1) + 1)^2 - 4
= (-2 + 1)^2 - 4
= (-1)^2 - 4
= 1 - 4
= -3
So, the y-coordinate is -3. This point satisfies the equation and lies on the graph.
Therefore, the correct point on the graph is (1,2).