Finding the Axis of Symmetry: y=(x-5)²+15 in Vertex Form

Question

What is the axis of symmetry of the equation?

$y=(x-5)^2+15$

00:00 Find the axis of symmetry of the function

00:05 We'll use the formula for representing a parabola

00:15 The axis of symmetry is on the X value of the vertex point (P)

00:19 We'll use the formula and find the term P

00:25 This is the axis of symmetry

00:28 And this is the solution to the question

The first step in solving the equation you presented:

y=(x-5)²+15

is to expand the parentheses:

y=x²-10x+25+15

y=x²-10x+40

From here, we can use the formula to find the X-coordinate of the vertex:

-b/2a

Let's substitute the values from the equation:

-(-10)/2*1 =

10/2=5

The axis of symmetry of the parabola is X=5

$x=5$