Find the vertex, focus, and directrix of the parabola with the gi...

Question

Find the vertex, focus, and directrix of the parabola with the given equation. Then graph the parabola. y^2 = 8x

Accepted Answer

Hello Today we're going to be using the given equation to identify the graph of the parabola. So what we are given is y squared is equal to 16 X. Now this equation is already given to us in the standard form of a parabola. And the standard form of this parabola is going to be y squared is equal to four P. X. This is the standard form of a parabola that opens a positively towards the X axis. So it's going to be opening up to the right hand side of the axis and this parabola is going to be located at the origin. So the vertex is going to be located at zero comma zero. So now that we know that the vote vertex is at the origin, we need to identify the focus. The focus is given to us as the focal constant for pete. And in the graph given to us 16 is going to equal to four P. So in order to figure out where the focus is located at, we're going to set four P equal to 16. And solving for P, we're going to divide both sides of this equation by four. That's going to give us P. Is equal to four. What this means is that the focus is located four points away from the vertex. So since the vertex is located at the origin and the graph is opening up to the to the positive side of the X axis. That means we're going to add four units to the X. Value of the vertex. So the focus is going to be located at zero plus four comma zero, which is going to give us the coordinate 00.4 comma zero. So this is gonna be the location of the focus and the direct tricks is going to be equal distance from the vertex, but it's going to be going the opposite direction of the focus. So since the focus is located for units to the right of the vertex, that means the direct tricks is going to be located four units to the left of the vertex. And the way we're going to represent that is X is equal to negative four. So now that we have the values of the direct tricks, the focus and the vertex, we just need to go ahead and select the graph that accurately represents these values and that graph is going to be option D. Here we can see that the vertex is located at zero comma zero. The graph opens up to the positive X direction and the focus is located at four comma zero. Furthermore, the direct tricks is equal distant from the center of the vertex, but it goes the opposite direction of the focus. So the origin of the direct tricks is going to be at negative four comma zero and this graph is represented as X is equal to negative four. With that being said, the answer to this problem is going to be D. So I hope this video helps you in understanding how to identify the graph of a parabola and I'll go ahead and see you all in the next video.

Find the vertex, focus, and directrix of the parabola with the given equation. Then graph the parabola. y^2 = 8x

Key Concepts

Parabola Definition

Vertex of a Parabola

Focus and Directrix

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