Modeling for Business: Part One — Test

Question 10 • Financial Math

Which graph represents the system of equations? y=x^2−2⁢x−3 y=−2⁢x+6

Answer

Image with description A coordinate plane with a line and a curved line. The x-axis is labeled from negative 4 to 5 and the y-axis is labeled from negative 20 to 30. Points on the line are (negative 3, 0), (0, 8), (2, 10). Points on the curved line are (negative 3, 0), (negative 1, negative 5), (1, 0), (4, 20).

Image with description A coordinate plane with a line and a curved line. The x-axis is labeled from negative 4 to 5 and the y-axis is labeled from negative 20 to 30. Points on the line are (negative 2, negative 10), (3, 0). Points on the curved line are (negative 1, 0), (3, 0).

Image with description A coordinate plane with a line and a curved line. The x-axis is labeled from negative 4 to 5 and the y-axis is labeled from negative 20 to 30. Points on the line are (negative 2, 10), (3, 0). Points on the curved line are (negative 1, 0), (3, 0).

Image with description A coordinate plane with a line and a curved line. The x-axis is labeled from negative 4 to 5 and the y-axis is labeled from negative 20 to 30. Points on the line are (negative 2, 10), (3, 0). Points on the curved line are (0, 0), (2, 0).

Explanation

The line y = −2x + 6 passes through (−2, 10) and (3, 0), since substituting those x-values gives y-values 10 and 0. The parabola y = x² − 2x − 3 factors as (x − 3)(x + 1), so its x-intercepts are (3, 0) and (−1, 0). Choice C shows both the line and parabola with these points.

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