Question

Describe the graph that would be used to solve the equation –x2 + 4 = x + 2 using a system of equations. How will you use the graph to find the solution(s)?

Answer 1

Edginuity Sample response: The graph consists of a parabola and a line. The parabola opens down and has a vertex of (0, 4). The line has a slope of 1 and a y-intercept of 2.

Answer 2

We want to solve
-x² + 4 = x + 2

Create two curves as follows:
y = -x² +4
and
y = x + 2

By graphing the two curves together, their points of intersection are the solutions.

y = -x² + 4 is a parabola with vertex at (0, 4), and it opens downward.
y = x + 2 is a straight line with slope - 1 and with y-intercept = 2
The points of intersection are (-2, 0) and (1, 3).

Answer:
The solutions are (-2, 0) and (1, 3).