Question

What is the axis of symmetry of -2x^2+5x+3 ?

Answer 1

`x = 5/4` or `x = 1.25`

Explanation:

There are several ways you could find this, but you are essentially finding the x-coordinate of the turning point of the parabola you have just given.

If we factorise the expression, we get `-2x^2 +5x + 3 = -(2x +1)(x -3)`.

We know that the turning point of the parabola occurs exactly half way between the roots (where the curve crosses the x-axis). To find the roots, we set the value of y equal to 0.

So `(2x + 1)(x-3) = 0, x = -1/2 and x = 3`

Now we just need to find the value of `x` which is halfway between these values of `x` we have just found, and we can do this by adding them together and then dividing by two.

So `(3 + (-1/2))/2 = (5/2)/2 = 5/4`

So the axis of symmetry (or line of symmetry) is `x = 5/4`