To write the given quadratic equation to its vertex form, we first form a perfect square.

x² - 2x + 5 = 0
Transpose the constant to other side of the equation,
x² - 2x = -5
Complete the square in the left side of the equation,
x² - 2x + (-2/1(2))² = -5 + (-2/1(2))²
Performed the operation,
x² - 2x + 1 = -5 + 1
Factor the left side of the equation,
(x - 1)² = -4

Thus, the vertex form of the equation is,
 (x-1)² + 4 = 0

4 0

3 years ago

Which statement is true about the domain of y = 3(2^-x)? Explain.

SVEN [57.7K]

We want to determine the domain of ${y=3 \cdot 2^{-x}=3 \cdot ({2^{-1}})^x=3 \cdot ({ \frac{1}{2}})^x$

any function of the form $y=f(x)=a \cdot b^x$ is called an "exponential function",
the only condition is that b is positive and different from 1, and a is a nonzero real number.

The domain of such functions is all real numbers.

That is for any x, the expression 3(2^-x) "makes sense".

Answer: The domain is all real numbers

8 0

3 years ago

Which of the following shapes are polygons with more than 444 sides?

Leviafan [203]

Hexagon and pentagon

6 0

3 years ago

Solve for X! Please help

WARRIOR [948]

The two given angles are vertical angles which mean they are the same:

9x + 72 = 4x + 112

Subtract 72 from bot sides:

9x = 4x + 40

Subtract 4x from both sides:

5x = 40

Divide both sides by 5:

X = 8

4 0

3 years ago