Which of the following is the vertex of the parabola which is the graph of the equation y = (x + 1)2 + 2?

Which of the following is the vertex of the parabola which is the graph of the equation y = (x + 1)2 + 2?
A . (C1, C2)
B . (1, C2)
C . (C1, 2)
D . (1, 2)
E . (2, C1)

View Answer

Answer: C

Explanation:

The equation of a parabola with its turning point c units to the left of the y-axis is written as y = (x + c)2. The equation of a parabola with its turning point d units above the x-axis is written as y = x2 + d. The vertex of the parabola formed by the equation y = (x + 1)2 + 2 is found one unit to the left of the y-axis and two units above the x-axis, at the point (C1, 2). Alternatively, test each answer choice by plugging the x value of the choice into the equation and solving for y. Only the coordinates in choice C, (C1, 2), represent a point on the parabola:

(y = (x + 1)2 + 2

2 = (C1 + 1)2 + 2,

2 = (0)2 + 2,

2 = 2

so it is the only point of the choices given that could be the vertex of the parabola.