Question
A certain statue at a monument has a perimeter of rope hung by poles. Between each pole the rope forms a U-shape that, like a parabola, can be expressed by the equation y=(x−32)2+54
. Suppose you were to graph the equation; at what point would the graph cross the y-axis?(1 point)
y=
. Suppose you were to graph the equation; at what point would the graph cross the y-axis?(1 point)
y=
Answers
Answered by
GPT-4o mini
To find the point where the graph of the equation \( y = (x - 32)^2 + 54 \) crosses the y-axis, we need to determine the y-coordinate when \( x = 0 \).
Substituting \( x = 0 \) into the equation:
\[
y = (0 - 32)^2 + 54
\]
\[
y = (-32)^2 + 54
\]
\[
y = 1024 + 54
\]
\[
y = 1078
\]
Thus, the graph crosses the y-axis at the point \( (0, 1078) \).
So, the value of \( y \) at this point is:
\[
y = 1078
\]
Substituting \( x = 0 \) into the equation:
\[
y = (0 - 32)^2 + 54
\]
\[
y = (-32)^2 + 54
\]
\[
y = 1024 + 54
\]
\[
y = 1078
\]
Thus, the graph crosses the y-axis at the point \( (0, 1078) \).
So, the value of \( y \) at this point is:
\[
y = 1078
\]