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

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

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

(0,−40)

Answer 1

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

The y-intercept occurs where \( x = 0 \). Let's calculate it:

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

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

Next, to find the point symmetrical to the y-intercept across the x-axis, we will change the sign of the y-coordinate while keeping the x-coordinate the same. Since the y-intercept is \( (0, -40) \), its symmetrical point will be \( (0, 40) \).

Looking at the provided options:

- (6, −40)
- (−6, −40)
- (0, 40) ← This is the correct answer!
- (0, −40)

Thus, the point that is symmetrical to the y-intercept is **(0, 40)**.