###### Answer: c. right

the directrix has the equation = … It is proved in a preceding section that if a parabola has its vertex at the origin and if it opens in the positive y direction then its equation is y = x 2 / 4f where f is its focal length. Comparing this with the last equation above shows that the focal length of the parabola …

At the vertex () = [] the radius of curvature equals R( 0 ) = 0 .5 (see figure). The parabola has fourth order contact with its osculating circle there. For large t the radius of curvature increases ~ t 3 that is the curve straightens more and more. Lissajous curve

Conic section – Wikipedia

Conic section – Wikipedia

Parabola – Wikipedia

Osculating circle – Wikipedia

If a < 0 the parabola has a maximum point and opens downward. The extreme point of the parabola whether minimum or maximum corresponds to its vertex . The x -coordinate of the vertex will be located at = − and the y-coordinate of the vertex may be found by substituting this x -value into the function. The y-intercept is located at the point ( 0 c). The solutions of the quadratic equation ax ... As an analogy suppose there was a section " x -intercept" in the article " Equation of a line". It seems clearer to me to have the statement If a line has an equation of the form y = mx + c then the x -intercept x 0 is -c / m. rather than If a line has an equation of the form y = mx + c then c = -mx 0 where x 0 is the x … For example a univariate (single-variable) quadratic function has the form = + + ≠in the single variable x .The graph of a univariate quadratic function is a parabola whose axis of symmetry is parallel to the y-axis as shown at right.. If the quadratic function is set equal to zero then the result is a quadratic equation .The solutions to the univariate equation are called the roots of the ... ...