Question

What is the equation of the absolute value function?

Answer 1

and explain.

Answer 2

to find the vertex of an absolute value expression, you'd first find the value for "x" that makes the absolute value expression = 0

say an example.... y = 3|x+5|-2

looking at the absolute value expression only, say x+5, what value of "x" makes that expresson = 0? well we could just do x + 5 = 0 => x = -5

so x = -5, makes the expression to 0, that is |(-5) +5| = | 0 |


so what's the vertex? well \(\bf y = 3|x+5|-2\\ \quad \\
y = 3|(\color{red}{-5})+5|\color{red}{-2}\\ \quad \\
(\color{red}{-5\quad ,\quad -2})\Longleftarrow vertex\)

Answer 3

notice the vertex of the function in the graph, is at ( -3, 4)

so the absolute value expression that = 0, when x = -3, is the x-coordinate


and the y-coordinate, well notice, is just "4"

Answer 4

@jdoe0001 I still don't understand