Answer:
x = 1
Step-by-step explanation:
The line of symmetry is defined as the x value of the vertex of a parabola.
To find the vertex of a parabola, we need to convert to vertex form.
Vertex form looks like this:
[tex]y=a(x-h)^2+k[/tex], where -h is the x value of the vertex and k is the y value of the vertex.
H is also defined as [tex]\frac{-b}{2a}[/tex] where a is the coefficient of x squared and b is the coefficient of the x term.
The coefficient of the x squared term is 1 and the coefficient of b is -2.
Plugging in, we get [tex]\frac{-(-2)}{2(1)}[/tex], which is equal to 1. This can then be plugged into the equation as
[tex]y=1(x-1)^2+k[/tex], but k doesn't matter because all we need is the x-term. Now, our x-term is negative h, which is negative negative one, which is positive one. Therefore, our answer is x = 1.
Answer:
x = 1
Step-by-step explanation:
Was the equation actually
f(x) = x² - 2x - 3
--------------------------
the line of symmetry occurs at the midpoint of the roots
factor
(x + 1)(x - 3)
x = { -1, 3}
midpoint of roots
x = (-1 + 3)/2
x = 1
line of symmetry
x = 1
