Locate the Vertex in the Parabola y=(x-3)²

Question

Find the vertex of the parabola

y=(x3)2 y=(x-3)^2

Video Solution

Solution Steps

00:00 Find the vertex of the parabola
00:03 Use the formula to describe the parabolic function
00:08 The coordinates of the vertex are (P,K)
00:12 Use this formula and find the vertex point
00:19 Substitute appropriate values according to the given data
00:24 And this is the solution to the problem

Step-by-Step Solution

To solve this problem, let's identify the vertex of the given parabola in the form y=(x3)2 y = (x - 3)^2 .

The parabola is already given in the vertex form of y=(xh)2+k y = (x - h)^2 + k , which is a special case of the quadratic equation where the vertex (h,kh, k) can be read directly from the equation.

  • Step 1: We compare the given equation y=(x3)2 y = (x - 3)^2 with the standard vertex form y=(xh)2+k y = (x - h)^2 + k .
  • Step 2: Notice that h=3 h = 3 and since there is no additional term added or subtracted outside the squared term, k=0 k = 0 .

Therefore, the vertex of the quadratic function y=(x3)2 y = (x - 3)^2 is (3,0) (3, 0) .

The correct choice from the multiple-choice options provided is the one that matches (3,0) (3, 0) .

The solution to the problem is the vertex (3,0) (3, 0) .

Answer

(3,0) (3,0)