Discover the Vertex of y=(x-1)²+3: A Parabola Challenge

Question

Find the vertex of the parabola

y=(x−1)2+3 y=(x-1)^2+3

Video Solution

Solution Steps

00:00 Find the vertex of the parabola
00:03 Use the formula to describe the parabolic function
00:10 The coordinates of the vertex are (P,K)
00:13 Use this formula and find the vertex point
00:16 Substitute appropriate values according to the given data
00:19 And this is the solution to the question

Step-by-Step Solution

To find the vertex of the parabola described by the equation y=(x−1)2+3 y = (x-1)^2 + 3 , we recognize that it is already in the vertex form y=a(x−h)2+k y = a(x-h)^2 + k .

Identify the components:

  • The expression (x−1) (x-1) indicates that h=1 h = 1 .
  • The constant term +3 +3 indicates that k=3 k = 3 .

The vertex of the parabola is the point (h,k) (h, k) .

Therefore, the vertex of the given parabola is (1,3) (1, 3) .

Answer

(1,3) (1,3)

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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