- Home
- ACCUPLACER Test Prep
- Conics
Conics - Parabola
- Lesson: 115:44
- Lesson: 220:25
- Lesson: 3a14:51
- Lesson: 3b9:14
- Lesson: 4a21:28
- Lesson: 4b13:19
- Lesson: 4c12:39
Conics - Parabola
Basic Concepts: Quadratic function in vertex form: y = a(x−p)2+q, Converting from general to vertex form by completing the square, Shortcut: Vertex formula, Graphing parabolas for given quadratic functions
Lessons
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
- 1.vertical parabola VS. horizontal parabola
Sketch the following vertical parabolas:
i) y=x2
ii) y=2x2
iii) y=2(x+3)2+1 - 2.Sketch the following horizontal parabolas:
i) x=y2
ii) x=21y2
iii) x=21(y−1)2−3 - 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.a)y=2x2−12x+10b)y2−10y−4x+13=0 - 4.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
a)y=81(x−6)2+3b)−12(x+1)=(y+4)2c)y2−10y−4x+13=0