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

What is the axis of symmetry of the equation?

y=(x−5)2+15 y=(x-5)^2+15

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Step-by-step video solution

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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

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

What is the axis of symmetry of the equation?

y=(x−5)2+15 y=(x-5)^2+15

2

Step-by-step solution

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

3

Final Answer

x=5 x=5

Practice Quiz

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Given the expression of the quadratic function

Finding the symmetry point of the function

\( f(x)=-5x^2+10 \)

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