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:The solutions are (-2 , 0) and (1 , 3) Step-by-step explanation:∵ -x² + 4 = x + 2* y = -x² + 4 ⇒ is quadratic represented by parabola  The parabola open downward because coefficient of x² is negative  The x-coordinate of its vertex = -b/2a, where b is the   coefficient of x and a is the coefficient of x²∴ x = 0/2(-1) = 0∴ The y-coordinate of the vertex = (0)² + 4 = 4∴ The maximum point of the parabola is (0 , 4)∵ -x² + 4 intersects x-axis at y = 0∴ -x² + 4 = 0 ⇒ -x² = -4 ⇒ x² = 4∵ x² = 4∴ x = ±√4 = ± 2∴ the parabola intersects x-axis at -2 , 2∵ y = x + 2 represented by a line its slope = 1   It intersects y-axis at 2∵ x + 2 intersects x-axis at y = 0∴ x + 2 = 0 ∴ x = -2∴ The parabola and the line intersect each other at   x = -2 and y = 0To find all the point of intersection between the 2 equations we will solve them as a system of equations∵ y= -x² + 4  and y = x + 2∴ -x² + 4 = x + 2∴ -x² + 4 - x - 2 = 0∴ -x² - x + 2 = 0 ⇒ × -1∴ x² + x - 2 = 0 ⇒ factorize∴ (x + 2)(x - 1) = 0∴ x + 2 = 0 ⇒ x = -2∴ x - 1 = 0 ⇒ x = 1* when x = -2 ⇒ y = -2 + 2 = 0 ⇒ (-2 , 0)* when x = 1 ⇒ y = 1 + 2 = 3 ⇒ (1 , 3)The solution graphically