Determine at sight the direction in which the curve opens. Locate the vertex, focus, and ends of the latus rectum: y^2 = 7x

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A parabola opens upwards if its general equation is of the form x^2 = 4ay and sidewards if its general equation is of the form y^2 = 4ay.

For y^2 = 4ax, the vertex is (0,0). For any other vertex (x0, y0) the equation is of the form (y -...

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A parabola opens upwards if its general equation is of the form x^2 = 4ay and sidewards if its general equation is of the form y^2 = 4ay.

For y^2 = 4ax, the vertex is (0,0). For any other vertex (x0, y0) the equation is of the form (y - y0)^2 = 4a(x - x0). So you can determine the vertex by seeing where the parabola intersects the axis. The focus is a point inside the parabola at a distance a from the vertex and lying on the axis.

The ends of the latus rectum are points of a chord drawn through the focus, parallel to the directrix which end on the parabola. For a parabola opening upward, they would have the same y-coordinate as the focus and the x-coordinate would be +2a and -2a.

For y^2 = 7x , a = 7/4

The parabola opens towards the right in the sidewards direction. The vertex is (0,0). The focus is (7/4, 0) and the ends of the latus rectum are (7/4, 7/2), and (7/4, -7/2).

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