Question

question 18 points 1

which of the following equations has the vertex (-2, 3)?

\\(y = -\sqrt3{x - 2} + 3\\)

\\(y = \sqrt3{x + 2} + 3\\)

Explanation:

Identify the vertex form of a cube root function

The general vertex form of a cube root function is:

$$y = a\sqrt[3]{x - h} + k$$

where \((h, k)\) represents the vertex (or point of inflection) of the function.

Substitute the given vertex into the general form

Given the vertex \((h, k) = (-2, 3)\), substitute \(h = -2\) and \(k = 3\) into the general equation:

$$y = a\sqrt[3]{x - (-2)} + 3$$

$$y = a\sqrt[3]{x + 2} + 3$$

Compare with the given options

We compare our derived form with the options shown in the image:

1. \(y = -\sqrt[3]{x - 2} + 3\) (vertex is \((2, 3)\))
2. \(y = \sqrt[3]{x + 2} + 3\) (vertex is \((-2, 3)\), matching with \(a = 1\))

Answer:

• (A) \(y = -\sqrt[3]{x - 2} + 3\)
• (B) \(y = \sqrt[3]{x + 2} + 3\) (Correct answer)