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Axis of Symmetry for a Quadratic

Axis of Symmetry for a Quadratic

The Axis of Symmetry lies halfway between the two roots for a quadratic graph.

Example 1

The function `4x^2-2x-2` factorises to `(2x+1)(2x-2)`.

Give the axis of symmetry to 2 decimal places.

The roots are at `x=-frac(1)(2)` and `x=1`

The Axis of Symmetry is halfway between at `x=0.25`

Graph of f(x)=4x<sup>2-2x-2 with axis of symmetry

Answer: `x=0.25`

Example 2

If the Axis of Symmetry for a quadratic is `x=-3.5`, and one root is `x=-5`, what is the other root given that the root must be greater than -3?

The distance between the root and the axis is 1.5. As the question states that the root is greater than -3, then `-3.5 + 1.5 = 2`.

Answer: `x=-2`