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

May 31, 2018

$x = \frac{5}{4}$ 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 $- 2 {x}^{2} + 5 x + 3 = - \left(2 x + 1\right) \left(x - 3\right)$.

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 $\left(2 x + 1\right) \left(x - 3\right) = 0 , x = - \frac{1}{2} \mathmr{and} x = 3$

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 $\frac{3 + \left(- \frac{1}{2}\right)}{2} = \frac{\frac{5}{2}}{2} = \frac{5}{4}$

So the axis of symmetry (or line of symmetry) is $x = \frac{5}{4}$