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−3/2)2+5/4

Question

. Suppose you were to graph the equation; at what point would the graph cross the y-axis?(1 point)
y=

Answer 1

To find the point where the graph of the equation \( y = \left(x - \frac{3}{2}\right)^2 + \frac{5}{4} \) crosses the y-axis, we set \( x = 0 \) because the y-axis corresponds to the value of \( x \) being zero.

Now we can substitute \( x = 0 \) into the equation:

\[ y = \left(0 - \frac{3}{2}\right)^2 + \frac{5}{4} \]

Calculating this step-by-step:

1. Compute \( 0 - \frac{3}{2} = -\frac{3}{2} \).
2. Square it: \[ \left(-\frac{3}{2}\right)^2 = \frac{9}{4} \]
3. Now, substitute back into the equation: \[ y = \frac{9}{4} + \frac{5}{4} \]
4. Combine the fractions: \[ y = \frac{9 + 5}{4} = \frac{14}{4} = \frac{7}{2} \]

Thus, the graph crosses the y-axis at:

\[ y = \frac{7}{2} \]

So the answer is \( y = \frac{7}{2} \).