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

00:07 Let's find the vertex of the parabola!
00:10 We use a special formula to describe a parabolic function.
00:15 The vertex has coordinates P comma K. Let's find them!
00:20 Apply this formula to discover the vertex point.
00:26 Substitute the right numbers from the data we have.
00:31 And, there you go! That's the solution to our 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)