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

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

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Answer 1 · 2018-05-31T12:37:30

$x = \frac{5}{4}$ $x = 5/4$ or $x = 1.25$ $x = 1.25$

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 $- 2 x^{2} + 5 x + 3 = - (2 x + 1) (x - 3)$ $-2x^2 +5x + 3 = -(2x +1)(x -3)$ .

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

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

So $\frac{3 + (- \frac{1}{2})}{2} = \frac{\frac{5}{2}}{2} = \frac{5}{4}$ $(3 + (-1/2))/2 = (5/2)/2 = 5/4$

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

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

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