Find the Vertex of y=(x-5)²+1: Parabola Analysis

Question

Find the vertex of the parabola

$y=(x-5)^2+1$

00:00 Find the vertex of the parabola

00:03 Use the formula to describe the parabola function

00:10 The coordinates of the vertex are (P,K)

00:14 Use this formula and find the vertex point

00:20 Substitute appropriate values according to the given data

00:23 And this is the solution to the question

To solve this problem, we will determine the vertex of the parabola from the equation $y = (x-5)^2 + 1$ , which is in vertex form.

Step 1: Recognize the form of the quadratic.
The given equation is $y = (x-5)^2 + 1$ , resembling the vertex form $y = a(x-h)^2 + k$ .
Step 2: Identify the vertex parameters $(h, k)$ .
In the equation $y = (x-5)^2 + 1$ :
$h = 5$ and $k = 1$ .
Step 3: Write down the coordinates of the vertex based on the identified values.
Therefore, the vertex of the parabola is at the point $(5, 1)$ .

Thus, the vertex of the parabola is $(5, 1)$ .

$(5,1)$