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25 votes
25 votes
Write the vertex form of the following function. (fill in each blank with the correct numerical

value: include the sign where needed)
An absolute value function with a vertex of (-12,10) and passes through the points (4, 6) and
(-8, 9).

Write the vertex form of the following function. (fill in each blank with the correct-example-1
User Arthur Ronconi
by
2.7k points

1 Answer

18 votes
18 votes

Answer:


-1/4 Abs(x+12) + 10

Explanation:

The vertex form of an absolute function is of the form
y = a|x -h| + k here |x-h| is the absolute value
where (h, k) are the coordinates (x, y) of the vertex

The vertex is given as (-12, 10)

So h = -12, k = 10

Plugging these in we get the vertex form as

y = a|x - (-12)| + 10

y = a|x + 12| + 10

All it remains is to find a

Given point (4, 6) as a point on the graph, plug these values
y = 6 = a|4 + 12| + 10

6 = a|16| + 10

6 = 16a + 10 since absolute value of a positive number is the number

Switch sides
16a + 10 = 6

Subtract 10 from both sides:
16a + 10 - 10 = 6 - 10
16a = -4
a = -1/4

So the equation of the function is
y = -1/4|x + 12| + 10

The second point is not needed to derive the function equation but let's use it to verify our calculated equation

Point (-8, 9)
Plug x = -8, into y = -1/4|x + 12| + 10

=> y = -1/4|-8+12| + 10
=> y = -(1/4)·4 + 10

=> y = -1 + 10

= y = 9 which matches with the y -coordinate of the second point

So everything looks cool

Final Solution
-1/4 Abs(x+12) + 10

For - 1/4 if it does not accept fractions, enter -0.25

I have also provided a screenshot which shows what should go into each box to help you out

Hope that helps and feel free to ask any clarifications



Write the vertex form of the following function. (fill in each blank with the correct-example-1
User Dpineda
by
2.5k points