Question

graph this function:
y = |x| - 9
click to plot the vertex first.

Explanation:

Step1: Identify the vertex form of absolute value function

The general form of an absolute value function is \( y = |x - h| + k \), where \((h, k)\) is the vertex. For the function \( y = |x| - 9 \), we can rewrite it as \( y = |x - 0| - 9 \). So, \( h = 0 \) and \( k = -9 \).

Step2: Plot the vertex

Using the values of \( h \) and \( k \), the vertex of the function \( y = |x| - 9 \) is at the point \((0, -9)\).

Step3: Find other points to graph the function

• When \( x = 1 \), \( y = |1| - 9 = 1 - 9 = -8 \), so the point is \((1, -8)\).
• When \( x = -1 \), \( y = |-1| - 9 = 1 - 9 = -8 \), so the point is \((-1, -8)\).
• When \( x = 2 \), \( y = |2| - 9 = 2 - 9 = -7 \), so the point is \((2, -7)\).
• When \( x = -2 \), \( y = |-2| - 9 = 2 - 9 = -7 \), so the point is \((-2, -7)\).

We can then plot these points and draw the V - shaped graph of the absolute value function.

Answer:

The vertex of the function \( y = |x| - 9 \) is at \((0, -9)\). To graph the function, plot the vertex \((0, -9)\) first, then plot other points like \((1, -8)\), \((-1, -8)\), \((2, -7)\), \((-2, -7)\) and draw the V - shaped graph.