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On a coordinate plane, an absolute value graph has a vertex at (-4, -10). Which equation represents the function graphed on the coordinate plane?

A. $ g(x) = |x + 4| - 10 $
B. $ g(x) = |x - 4| - 10 $
C. $ g(x) = |x - 10| + 4 $
D. $ g(x) = |x + 10| - 4 $

Question

High School

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Answer :

vaishnavim26 vaishnavim26 · Answer 1 · 2024-09-20T17:35:50-04:00

The correct equation that represents the function graphed on the coordinate plane is g(x) = |x - 4| - 10.

The equation that represents the function graphed on the coordinate plane with a vertex at (-4, -10) is:

g(x) = |x - 4| - 10

Let's break down the equation to understand why it represents the absolute value graph with the given vertex:

The general form of an absolute value function is f(x) = |ax + b| + c, where a, b, and c are constants.

In this case, the vertex of the graph is (-4, -10), which means that when x = -4, the function has its minimum value of -10.

To achieve the vertex at (-4, -10), we need to have the expression |ax + b| equal to 0 when x = -4. To do this, we set ax + b = 0 and solve for b:

-4a + b = 0

b = 4a

Now, we know that when x = -4, the function has its minimum value of -10. Plugging these values into the absolute value function, we have:

f(-4) = |a(-4) + b| + c = |-4a + 4a| + c = 0 + c = -10

Therefore, c = -10.

Now we have a = 1 and c = -10. Substituting these values back into the general form of the absolute value function, we get:

g(x) = |x - 4| - 10

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