Find the Vertex: Analyzing y = (x-3)² - 10

Question

Find the vertex of the parabola

$y=(x-3)^2-10$

00:00 Find the vertex coordinates of the parabola

00:03 Use the formula to describe the parabola function

00:08 The vertex coordinates are (P,K)

00:13 Use this formula and find the vertex coordinates

00:18 Substitute appropriate values according to the given data

00:22 And this is the solution to the question

To solve this problem, we'll find the vertex of the parabola given by the function $y = (x-3)^2 - 10$ .

Step 1: Recognize the function's form. The equation is written in the vertex form of a quadratic function: $y = a(x-h)^2 + k$ .
Step 2: Identify the values of $h$ and $k$ from the function. Here, $(x-3)^2$ indicates that $h = 3$ and the $-10$ outside the square indicates $k = -10$ .

By substituting into the vertex form, we see that the vertex of the parabola is $(h, k) = (3, -10)$ .

Therefore, the vertex of the parabola is $(3, -10)$ .

$(3,-10)$