Question

How do you find the intercepts and vertex for `y=-2|5x+8|+4`?

Answer 1

Intercepts: `x = -6/5` ; and `x = 6/5`
Vertex: (0, -12)

Explanation:

At x = 0, y = -12. The absolute value function just means that the graph will be symmetric about some point, forming a “V” shape in the case of a linear equation. The x intercepts are:
`−2|5x+8|+4 = 0` ; `−2|5x+8| = -4` ; `|5x+8| = 2` ; `+(5x+8) = 2` and `-(5x+8) = 2` ;
`5x = -6` ; `x = -6/5` and `-5x = -6`; `x = 6/5`
The vertex must be the point midway between these two for the linear symmetry. That will be the point at x = 0, where we have already found y to be -12.