Question

describe the key features of a parabola with the equation $x^2 = 40y$. the value of $p$ is 10. the parabola opens dropdown with options down, left, right, up. the coordinates of thcut off are dropdown. the equation for the cut off is dropdown.

Explanation:

Step1: Recall the standard form of a parabola

The standard form of a parabola that opens up or down is \(x^{2}=4py\), where \(p\) is the distance from the vertex to the focus (and also from the vertex to the directrix). If \(p>0\), the parabola opens up; if \(p < 0\), it opens down.

Step2: Analyze the given equation

The given equation is \(x^{2}=40y\). Comparing it with the standard form \(x^{2}=4py\), we can see that \(4p = 40\), so \(p=\frac{40}{4}=10\). Since \(p = 10>0\), the parabola opens up.

Answer:

up