Writing Equations of Parabolas. Parabola focus Axis of symmetry vertex directrix p p.

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Presentation transcript:

Writing Equations of Parabolas

Parabola focus Axis of symmetry vertex directrix p p

Standard Eq. of Parabola EquationFocusDirectri x Axis of Symmetry (x-h) 2 =-4p(y-k) Opening down if p<0 (h,k+p)y = k-pVertical (x-h) 2 =4p(y-k) Opening up if p>0 (h,k+p)y = k–pVertical (y-k) 2 =4p(x-h) Opening right if p>0 (h+p,k)x=h-pHorizontal (y-k) 2 =-4p(x-h) Opening left if p<0 (h+p,k)x = h-pHorizontal

Example Write an equation for a parabola in standard form with vertex at (0,0) and directrix y = -3/2.

Example Write an equation in standard form of the parabola with vertex at (0,0) and directrix x = 3.

Example Write an equation for a parabola in standard form with vertex at (0,0) and focus at (-5,0).

Example Write an equation of a parabola in standard form with vertex at (0,0) and focus at (0,-10).

Example Write an equation of a parabola that passes through the point at (2,-1), has its vertex at (-7,5), and opens to the right.

Example Write an equation for the parabola that passes through the point (5,2), has a vertical axis, and has a minimum at (4,-3).