Question

Which equation could represent the graph shown below?

Answer 1

The equation of the graph is $f(x) = -\sqrt{x -2$

How to determine the graph equation?

The graph is added as an attachment

The form of the graph is

$f(x) = a\sqrt{x + b$

The graph passes through the points (2, 0) and (6, -2).

So, we have:

$0 = a\sqrt{2 + b$ and $-2 = a\sqrt{6 + b$

Solve for b in $0 = a\sqrt{2 + b$

Divide both sides by a

$0 = \sqrt{2 + b$

Square both sides

0 = 2 + b

Subtract 2 from both sides

b = -2

Substitute b = -2 in $-2 = a\sqrt{6 + b$

$-2 = a\sqrt{6 -2$

$-2 = a\sqrt{4$

Evaluate the square root

-2 = 2a

Divide by 2

a = -1

Substitute b = -2 and a = -1 in $f(x) = a\sqrt{x + b$

$f(x) = -\sqrt{x -2$

Hence, the equation of the graph is $f(x) = -\sqrt{x -2$

Read more about functions at:

brainly.com/question/13810353

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