The boundaries are given by the x-intercepts of the graph of the corresponding function.
No, see solution.
Practice makes perfect
Recall that the boundaries are given by the x-intercepts of the graph of the corresponding function. We can find them by finding the zeroes of the quadratic equations. Let's have a look at our inequalities.
Inequality (I) Inequality (II) [0.8em]
x^2+4x-12 ≤ 0 1/2x^2+2x-6 ≤ 0 [1.3em]
Corresponding Functions [0.8em]
y = x^2+4x-12 y = 1/2x^2+2x-6 [1.3em]
Corresponding Equations [0.8em]
x^2+4x-12 = 0 1/2x^2+2x-6 = 0 [1.3em]Notice that if we multiply the corresponding equation of Inequality (II) by 2, we obtain the same equation as that corresponding to Inequality (I).
( 12x^2+2x-6 = 0)* 2
⇓
x^2+4x-12 = 0
This means that they will have the same solutions, and therefore their corresponding functions will have the same x-intercepts. We can graph both functions to see this explicitly.
Therefore, the boundaries for both solution sets are the same.
