The graphs below have the same shape. What is the equation of the red graph?

Mathematics

1 answer:

VARVARA [1.3K]1 year ago

5 0

Answer:

$G(x) = x^{3} -1$

Step-by-step explanation:

The red graph is the blue graph translated 1 unit down, so the answer is A.

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Hey!

To solve x in this equation we must first add five to both sides to get $\sqrt{x}$ on its own.

Original Equation :
$\sqrt{x} - 5 = x - 11$

New Equation {Added 5 to Both Sides} :
$\sqrt{x} =x-6$

Now we must square both sides of the equation.

Old Equation :
$\sqrt{x} =x-6$

New Equation {Changed by Squaring Both Sides} :
$x= x^{2} -12x+36$

And now we must solve the new equation.

Step 1 - Switch sides
$x^{2} -12x+36=x$

Step 2 - Subtract x from both sides
$x^{2} -12x+36-x=x-x$

Step 3 - Simplify
$x^{2} -13x+36=0$

Now we need to solve the rest of the equation using the quadratic formula.

$\frac{-(-13)+ \sqrt{(-13) ^{2}-4*1*36 } }{2*1}$

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$\frac{13+ \sqrt{25}}{2}$

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$\frac{-(-13)- \sqrt{(-13) ^{2} -4*1*36} }{2*1}$

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