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* x*(1)/(2)+\left((1)/(2)\right)^2\right)+3+\left((1)/(2)\right)^2\\\\\\\Rightarrow y=-\left(x-(1)/(2)\right)^2+3+(1)/(4)\\\\\\\Rightarrow y=-\left(x-(1)/(2)\right)+(13)/(4).`

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

`x-(1)/(2)=0\\\\\Rightarrow 2x-1=0`

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