How do you solve -x^2+x+5>0 by graphing?

1 Answer
Nov 21, 2016

-1.791 < x < 2.791
graph{-x^2+x +5 [-10, 10, -5, 5]}

Explanation:

Find the points of intersection of the graph with the x-axis.

- x^2 + x + 5 = 0

using x = ( -b +- sqrt(b^2 - 4ac))/ (-2a)

x = ( -1 +- sqrt(1^2 - 4(-1)5))/ (-2(-1))

x = ( -1 +- sqrt(21))/ 2

x = -1.791, 2.791

The point of intersection of the graph with y-axis
is y = 5 by substituting x = 0 into - x^2 + x + 5

Since the coefficient of x^2 is negative, the curve upwards, as shown in the graph.

For - x^2 + x + 5 > 0 , we look at the region of the graph where the curve is above the y-axis.

Hence, -1.791 < x < 2.791