Question

What is the line of symmetry for the parabola whose equation is y = -x2 + x + 3?

Answer 1

Alright so if I do remember my math correctly, this is how it goes:

- y = -x^2 + x + 3

- x = -b/2a

- x = -1/2(-1)

- x = -1/-2, which = (1/2)

Not quite sure if this was correct, but if it was, hope this helps and you're welcome! :)

Answer 2

Answer:  The required line of symmetry of the given parabola is $2x-1=0.$

Step-by-step explanation:  We are given to find the line of symmetry for the parabola with the following equation :

$y=-x^2+x+3~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

We know that

the STANDARD equation of a parabola is given by

$y=a(x-h)^2+k,$

where the line of symmetry is x - h = 0.

From equation (i), we get

$y=-x^2+x+3\\\\\Rightarrow y=-(x^2-x)+3\\\\\Rightarrow y=-\left(x^2-2\times x\times\dfrac{1}{2}+\left(\dfrac{1}{2}\right)^2\right)+3+\left(\dfrac{1}{2}\right)^2\\\\\\\Rightarrow y=-\left(x-\dfrac{1}{2}\right)^2+3+\dfrac{1}{4}\\\\\\\Rightarrow y=-\left(x-\dfrac{1}{2}\right)+\dfrac{13}{4}.$

Comparing with the standard form of the parabola, the line of symmetry is given by

$x-\dfrac{1}{2}=0\\\\\Rightarrow 2x-1=0$

Thus, the required line of symmetry of the given parabola is $2x-1=0.$