Find the Vertex of y=(x+2)²-2: Quadratic Function Analysis

Question

Find the vertex of the parabola

y=(x+2)2−2 y=(x+2)^2-2

Video Solution

Solution Steps

00:00 Find the vertex of the parabola
00:03 We'll use the formula to describe the parabola function
00:08 The coordinates of the vertex are (P,K)
00:12 We'll use this formula and find the vertex point
00:16 We notice that according to the formula, the term P is negative
00:27 We'll substitute appropriate values according to the given data
00:30 And this is the solution to the question

Step-by-Step Solution

To solve the problem of finding the vertex of the parabola represented by y=(x+2)2−2 y = (x+2)^2 - 2 , consider the form of the equation.

This equation is written in the vertex form of a quadratic function, which is given by:

y=a(x−h)2+k y = a(x-h)^2 + k

where (h,k) (h, k) is the vertex of the parabola.

Comparing y=(x+2)2−2 y = (x+2)^2 - 2 with the standard form y=a(x−h)2+k y = a(x-h)^2 + k , we identify:

  • h=−2 h = -2 because the expression is (x−(−2))2 (x - (-2))^2
  • k=−2 k = -2

Therefore, the vertex of the parabola is (−2,−2)(-2, -2).

The correct answer is (−2,−2)(-2, -2).

Answer

(−2,−2) (-2,-2)

More Questions

Related Subjects

Vertex form of the quadratic equation Vertex of a parabola Ways to represent a quadratic function

Question Types

Vertex Representation: Linking function properties to its representation The Vertex of the Parabola: Linking function properties to its representation