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

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)



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. =)