2. Section 2.3
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Using the graphing form, the vertex and line of symmetry can both be found.
Using the graphing form, the vertex and line of symmetry can both be found.
Graphing Form: y=2(x-2)^2-1
Vertex: (2,- 1)
Line of Symmetry: x=2
Graphing Form: y=5(x-1)^2-12
Vertex: (1,- 12)
Line of Symmetry: x=1
Let's rewrite the function in graphing form by completing the square.
Split into factors
Factor out 2
Complete the square
Calculate quotient
(- a)^2=a^2
Split into factors
a^2-2ab+b^2=(a-b)^2
Multiply
Subtract term
Having rewritten the function in graphing form, we can identify the vertex and line of symmetry. y=2(x- 2)^2+ 3 [-1em] &Vertex: ( 2, 3) &Line of Symmetry: x_s= 2
Like in Part A, we will rewrite the equation in graphing form by completing the square.
Split into factors
Factor out 5
Complete the square
Calculate quotient
(- a)^2=a^2
Split into factors
a^2-2ab+b^2=(a-b)^2
Identity Property of Multiplication
Subtract term
Having rewritten the function in graphing form, we can identify the vertex and line of symmetry. y=5(x- 1)^2 - 12 [-1em] &Vertex: ( 1, -12) &Line of Symmetry: x_s= 1