Determine the Vertex of the Parabola: y = (x-3)² - 1

Question

Find the vertex of the parabola

y=(x−3)2−1 y=(x-3)^2-1

Video Solution

Solution Steps

00:00 Find the vertex of the parabola
00:03 Use the formula to describe the parabola function
00:07 The coordinates of the vertex are (P,K)
00:11 Use this formula and find the vertex point
00:14 Substitute appropriate values according to the given data
00:19 And this is the solution to the question

Step-by-Step Solution

To solve for the vertex of the parabola given by the equation y=(x−3)2−1 y = (x-3)^2 - 1 , we start by comparing the equation with the standard vertex form of a quadratic function: y=a(x−h)2+k y = a(x-h)^2 + k .

In the given equation, y=(x−3)2−1 y = (x-3)^2 - 1 , we identify:
- h=3 h = 3 , which corresponds to the horizontal shift of the parabola.
- k=−1 k = -1 , which represents the vertical shift.

Therefore, the vertex of the parabola is at the point (h,k)(h, k), which is (3,−1)(3, -1).

Thus, the vertex of the parabola is (3,−1)(3, -1).

Answer

(3,−1) (3,-1)

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Related Subjects

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

Question Types

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