Answer:
[tex]f(x) = -\frac{2}{5} |x + 1| + 3[/tex]
Step-by-step explanation:
The formula for the absolute value function in vertex form is:
f(x)= a|x – h| + k
where:
(h, k) = vertex
a = determines whether the graph opens up or down.
h = determines how far left or right the parent function is translated.
k = determines how far up or down the parent function is translated.
Given the value of the vertex, (-1, 3), substitute its values into the vertex form:
f(x)= a|x – h| + k
f(x)= a|x + 1| + 3
Next, use the other given point, (4, 1) to solve for "a":
1= a|4 + 1| + 3
1 = a|5| + 3
1 = 5a + 3
Subtract 3 from both sides:
1 - 3 = 5a + 3 - 3
-2 = 5a
Divide both sdies by 5:
[tex]\frac{-2}{5} = \frac{5a}{5}[/tex]
[tex]-\frac{2}{5}[/tex] = a
Therefore, the equation of an absolute value function is: [tex]f(x) = -\frac{2}{5} |x + 1| + 3[/tex]
