Question

The line of symmetry of the parabola whose equation is y = ax2 - 4x + 3 is x = -2. What is the value of "a"?

A. -2
B. -1
C. -1/2

Answer 1

Can you find the vertex of y=ax^2-4x+3?

Answer 2

the line of symmetry will go through the vertex

Answer 3

I wouldn't know how to find it.

Answer 4

Well there should have been a formula derived for you to find the vertex of a parabola.
It involves completing the square.

Answer 5

\[y=ax^2+bx+c \\ y=ax^2+\frac{a}{a}bx+c \\ y=a(x^2+\frac{1}{a}bx)+c \\ y=a(x^2+\frac{b}{a}x)+c \\ y=a(x^2+\frac{b}{a} x+(\frac{b}{2a})^2)+c-a(\frac{b}{2a})^2 \\ y=a(x+\frac{b}{2a})^2+c-a \frac{b^2}{4a^2} \\ y=a(x+\frac{b}{2a})^2+c-\frac{b^2}{4a} \]
The x-coordinate of the vertex is -b/(2a)

Answer 6

I'm still lost....

Answer 7

On what vertex means?
Or that the axis of symmetry goes through the vertex?

Answer 8

Both really, all the algebra I've been doing that had something to with graphing I haven't understood.

Answer 9

Here is an example:
The axis of symmetry of
\[y=-2(x+3)^2+54\]
is x=-3 and the vertex is (-3,54)

Do you see why the axis of symmetry is x=-3. (notice the x-coordinate of the vertex is -3)
It is because you can fold your graph about that line and the opposite part of the graph lays perfectly on the other part.

For your problem you have the axis of symmetry is -b/(2a) where your vertex's x coordinate is -2.
As in the above example they must be the same number (well since this is a vertical parabola and therefore all axis of symmetry are in the from x=number).