Question

What point is symmetrical to the y-intercept of y=x2−6x−40
?(1 point)
Responses

(6,−40)
left parenthesis 6 comma negative 40 right parenthesis

(0,40)
left parenthesis 0 comma 40 right parenthesis

(−6,−40)
left parenthesis negative 6 comma negative 40 right parenthesis

(0,−40)

Answer 1

To find the point symmetrical to the y-intercept of the function \( y = x^2 - 6x - 40 \), we first need to determine the y-intercept of the given quadratic equation.

The y-intercept occurs when \( x = 0 \):

\[
y = 0^2 - 6(0) - 40 = -40
\]

So, the y-intercept is the point \( (0, -40) \).

To find a point that is symmetrical to this point across the y-axis, we need to reflect the point across the y-axis. The reflection of the point \( (x, y) \) will be \( (-x, y) \).

Reflecting \( (0, -40) \) gives us the point \( (0, -40) \) (since the x-coordinate is 0 and does not change).

Now, looking at your response options, we see that \( (0, -40) \) is one of the choices.

Therefore, the point that is symmetrical to the y-intercept \( (0, -40) \) is:

\[
\boxed{(0, -40)}
\]