Conics - Parabola
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Examples
Lessons
- vertical parabola VS. horizontal parabola
Sketch the following vertical parabolas:
i) y=x2
ii) y=2x2
iii) y=2(x+3)2+1 - Sketch the following horizontal parabolas:
i) x=y2
ii) x=21y2
iii) x=21(y−1)2−3 - converting quadratic functions to vertex form by "completing the square"
Convert each quadratic function from general form to vertex form by completing the square. - finding the focus and directrix using the formula: p=4a1
For each quadratic function, state the:
i) vertex
ii) axis of symmetry
iii) focus
iv) directrix
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Topic Notes
parabola: a curve formed from all the points that are equidistant from the focus and the directrix.
vertex: midway between the focus and the directrix
focus: a point inside the parabola
directrix: a line outside the parabola and perpendicular to the axis of symmetry
conics formula for parabola:
p=4a1 p: distance between the vertex and the focus / directrix.
a: coefficient of the squared term
vertex: midway between the focus and the directrix
focus: a point inside the parabola
directrix: a line outside the parabola and perpendicular to the axis of symmetry
conics formula for parabola:
p=4a1 p: distance between the vertex and the focus / directrix.
a: coefficient of the squared term
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