Given a quadratic function
f(x) = ax^2 + bx + c (a != 0),
the line of symmetry.of this function's graph is a vertical line, whose equation is
x = xv
where xv is the x-coordinate of the vertex, given by
xv = - b/(2a)
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For this question, you have this function:
f(x) = ax^2 - 4x + 3
so the coefficient b is - 4.
Also, the value of the x-coordinate of the vertex is known (from the line of symmetry):
xv = - 2
So you must have
- b/(2a) = - 2
Multiply both sides by 2a, and you get
- b = 2a * (- 2)
- b = - 4a
Divide both sides by - 4, so you get the a isolated:
a = - b/(- 4)
a = b/4
Now, just plug in the expression above the value of b, and you finally get
a = - 4/4
a = - 1 <---- and there it is.
I hope this helps. =)