Question

The line of symmetry of the parabola whose equation is `y=ax^2-4x+ 3` is `x=-2`. What is the value of "a"?

Answer 1

`a=-1`

Explanation:

The line or axis of symmetry is given by the formula

`x=-b/(2a)`

You are told that the line of symmetry is `x=-2`. This means that you can replace the letter `x` by the number `-2`.
`-2=-b/(2a)`

The parabola, `y=ax^2-4x+3`, has `b=-4`. You can plug `b=-4` into the line of symmetry formula.

`-2=(-(-4))/(2(a))`
`-2=4/(2a)` (negative times negative is positive)
`-2a=4/2` (multiply both sides by `a`)
`-2a=2`
`a=-1` (divide both sides by -2)

Answer 2

`a = -1`

Explanation:

Completing the square, we have:

`y = a(x^2 - 4/a) + 3`

`y = a(x^2 - 4/a + 4/a^2 - 4/a^2) + 3`

`y = a(x^2 - 4/a + 4/a^2) - 4/a + 3`

`y = a(x - 2/a)^2 - 4/a + 3`

If the vertex is at `(C, D)`, then the axis of symmetry is `x = C`. Also, the vertex in the form `y = a(x- p)^2 + q` is given by `(p, q)`. Therefore, the axis of symmetry is `x = 2/a`. Since it's given that it's `x = -2`, we have:

`-2 = 2/a`

`-2a = 2`

`a = -1`

Hopefully this helps!