Question

Can someone please tell me the answer to this question?

Answer 1

The value of constant a is -3.

Curve $y=-1+\sqrt{x+4}$ is shown on the line y = 3.

We have to show that the curve can be rearranged as $x=y^2+2y+a$ where we have to find the constant a.

We have the given curve:-

$y=-1+\sqrt{x+4}$

Adding 1 on both sides of the equation, we get

y + 1 = $\sqrt{x+4}$

Squaring the equation on both sides, we get,

$(y+1)^2=(\sqrt{x+4} )^2$

$y^2+2y+1$ = x  + 4

Subtracting 4 from both the sides of the equation, we get,

x = $y^2+2y+1-4$.

x = $y^2+2y-3$

Hence, we have shown the curve in the form of $x=y^2+2y+a$.

Now,

Comparing it with $x=y^2+2y+a$, we get,

a = -3.

To learn more about equation, here:-

brainly.com/question/10413253

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