Question

Find the line of symmetry equation for the function f(x )=x −2x −3.

Answer 1

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:

$y=a(x-h)^2+k$, where -h is the x value of the vertex and k is the y value of the vertex.

H is also defined as $\frac{-b}{2a}$ 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 $\frac{-(-2)}{2(1)}$, which is equal to 1. This can then be plugged into the equation as

$y=1(x-1)^2+k$, 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 2

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