Solving One-Variable Equations with Systems — Quiz

Question 8 • Mathematics III

Which graph can be used to find the solution(s) to x squared minus 1 is equal to x plus 1 ?

Answer

Image with description On a coordinate plane, the scale on the x and y axes ranges from negative 5 to 5 with an interval of 1 unit. A line passes through the origin and (1 comma 1). A parabola opens up, has vertex at (0 comma negative 1) and cuts the x-axis at (negative 1 comma 0) and (1 comma 0).

Image with description On a coordinate plane, the scale on the x and y axes ranges from negative 5 to 5 with an interval of 1 unit. A line passes through (0 comma 1) and (negative 1 comma 0). A parabola opens up, has vertex at (0 comma negative 1) and cuts the x axis at (negative 1 comma 0) and (1 comma 0).

Image with description On a coordinate plane, the scale on the x and y axes ranges from negative 5 to 5 with an interval of 1 unit. A line passes through (0 comma 1) and (negative 1 comma 0). A parabola opens down, has vertex at (0 comma 1) and cuts the x axis at (negative 1 comma 0) and (1 comma 0).

Image with description On a coordinate plane, the scale on the x and y axes ranges from negative 5 to 5 with an interval of 1 unit. A line passes through the origin and (1 comma 1). A parabola opens down, has vertex at (0 comma 1) and cuts the x axis at (negative 1 comma 0) and (1 comma 0).

Explanation

Graph the two sides as y = x² − 1 and y = x + 1. The parabola y = x² − 1 opens upward, has vertex (0, −1), and crosses the x-axis at −1 and 1. The line y = x + 1 passes through (0, 1) and (−1, 0), which matches choice B; their intersection points give the solutions.

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