<\/span><\/h2>\nTo determine the vertex of an absolute value equation without graphing, you can follow these simple steps:<\/p>\n
Step 1:<\/b> Identify the values of a, h, and k in the equation.
\nThe equation should be in the form |x – h| + k = c. The value of (h, k) corresponds to the coordinates of the vertex.<\/p>\n
Step 2:<\/b> Set the expression inside the absolute value notation, x – h, equal to zero and solve for x.
\nBy setting x – h = 0, you isolate x and find the value of h.<\/p>\n
Step 3:<\/b> Substitute the value of h obtained in step 2 back into the original equation.
\nReplace h with its value in the equation, resulting in |x – h| + k = c.<\/p>\n
Step 4:<\/b> Solve for k.
\nSince the absolute value of (x – h) is equal to zero when x = h, the equation becomes |0| + k = c. Simplifying further, you find that k = c.<\/p>\n
Step 5:<\/b> The vertex of the absolute value equation is given by (h, k).
\nAfter obtaining the values of h and k, you can determine the vertex, which represents the maximum or minimum point on the graph.<\/p>\n
The answer to the question “How to find the vertex of an absolute value equation without graphing?” is:<\/b> By following the steps above, you can find the vertex of an absolute value equation without having to construct a graph.<\/p>\n