Solving One-Variable Equations with Systems — Quiz

Question 9 • Mathematics III

Which graph can be used to find the solution(s) to x squared minus 1 is equal to 3 ?

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 (negative 3 comma 0) and (0 comma 3). 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 9 to 9 with an interval of 1 unit. A line is parallel to the x axis and cuts the y axis at (0 comma 3). A parabola opens up, has vertex (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 9 to 9 with an interval of 1 unit. A line is parallel to the y axis and cuts the x axis at (3 comma 0). A parabola opens up, has vertex (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 9 to 9 with an interval of 1 unit. A line passes through the origin and (1 comma 3). A parabola opens up, has a vertex (0 comma negative 1) and cuts the x axis at (negative 1 comma 0) and (1 comma 0).

Explanation

To solve x² − 1 = 3 by graphing, compare the graph of y = x² − 1 with the graph of y = 3. The first is an upward-opening parabola with vertex (0, −1), and the second is a horizontal line crossing the y-axis at 3. Their intersection points have x-coordinates that solve the equation, so the graph described in choice A can be used.

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