What is the line of symmetry for the parabola whose equation is y=2x^2-4x+1?

Mignolij6s

Mignolij6s

Answered question

2022-12-24

What is the line of symmetry for the parabola whose equation is #y=2x^2-4x+1#?

Answer & Explanation

Jaqueline Byrd

Jaqueline Byrd

Beginner2022-12-25Added 4 answers

Calculus approach.
y=2x24x+1
dydx=4x4
Where the curve turns will be the line of symmetry (due to the nature of the x2 graph).
This is also when the gradient of the curve is 0.
Then, let dydx=0
This forms an equation such that:
4x4=0
solve for x, x=1 and line of symmetry falls on the line x=1
Irene Carter

Irene Carter

Beginner2022-12-26Added 1 answers

Algebraic approach.
To find the turning points, fill in the square as follows:
y=2(x22x+12)
y=2((x1)21+12)
y=2(x1)21
We can determine the line of symmetry from this in the following way:
x=1

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