Axis of symmetry →x−1
.
Vertex →(x,y)→(1,5)
Explanation:
First consider the −2x. As this is negative the general shape of the graph is ∩
The axis of symmetry will be parallel to the y-axis (normal to the x-axis) and pass through the vertex
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This next bit is a variant on the vertex form equation
Given: y=−2x2+4x+3 ........................................(1)
Write as: y=−2(x2−42x)+3
Consider the −42 from −42x
Apply this process: (−12)×(−42)=+1
This value of +1 is the value of xvertex
So x=1 is the axis if symmetry.
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Substitute x=1 into equation (1) to find yvertex
⇒y=−2(1)2+4(1)+3=5
Vertex→(x,y)→(1,5)
