y = |x − 4| + 8
Find the x-coordinate of the vertex of
the graph.
And the y-coordinate of the vertex of the graph.
Please help me, I'm stuck!
you have to put it into a vertex form
y=a(x-h)^2 +k
y=x+4(because of sign ||)+8
now you have to get ^2
y=a(.5x-2)^2+8
y=1(.5x-2)^2+8
now k shifts up or down IE y axis
h shifts left or right IE x axis but a +h=-h and a -h=+h so your vertex would be (2,8) because h is -2 and k is 8
To find the x-coordinate of the vertex of the graph of the equation y = |x − 4| + 8, we need to remember that the vertex of an absolute value function, in the form y = |x − h| + k, is located at (h, k).
In this case, the equation is already in the correct form, so we can determine the x-coordinate of the vertex by setting the expression inside the absolute value bars equal to zero and solving for x.
Setting x − 4 equal to zero, we get:
x − 4 = 0
Solving for x, we add 4 to both sides of the equation:
x = 4
Therefore, the x-coordinate of the vertex is 4.
Now, to find the y-coordinate of the vertex, we substitute the x-coordinate (4) back into the equation:
y = |4 − 4| + 8
y = |0| + 8
y = 0 + 8
y = 8
Hence, the y-coordinate of the vertex is 8.
Therefore, the vertex of the graph of y = |x − 4| + 8 is (4, 8).