Question

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Answer 1

Axis of symmetry →x−1

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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)