What is the vertex of the graph of y = |x + 3|?
I went to freemathhelp and this is what I got:
*Not a conic section.
That is correct, but that doesn't mean there's no vertex.
Absolute value graphs usually have a V-shape, because |N| is always positive. So, if you have a line sloping down to the x-axis, when it reaches y=0, it reflects back up, so that it always stays with y>=0.
So, |x+3| = x+3 if x+3 >= 0
But |x+3| = -x-3 is x+3 < 0
So, where x = -3, the graph has a point, or vertex. Go back online and find a graphing tool. Or, check out some example graphs of absolute value functions.
To find the vertex of the graph of the function y = |x + 3|, you need to understand that the vertex occurs at the point where the absolute value function changes its direction. Here's how you can find the vertex:
Step 1: Set the expression inside the absolute value bars equal to zero.
x + 3 = 0
Step 2: Solve for x.
x = -3
Step 3: Substitute the value of x into the original equation to find the corresponding y-coordinate.
y = |-3 + 3|
y = |0|
y = 0
Step 4: The vertex of the graph is the coordinate (-3, 0).
So, the vertex of the graph of y = |x + 3| is (-3, 0).