Characteristics and G
Parabolas that Open Upwards
Form : 4 p( y − k) = (x − h)2 (note “x” part is squared)
Find the characteristics and graph: 8( y − 3) = (x + 1)2 .
Vertex Do the opposite of the numbers y=
(point) with x and y.
Point on Pick a value right next to the
Parabola vertex and plug into the equation.
Mirror this point.
Focus Go directly above the vertex a
(point) length of “p.”
Directrix A horizontal line that is “p”
(line) directly below the vertex.
Graphs of Parabolas
Parabolas that Open Downwards
Form : −4 p( y − k) = (x − h)2 (note the added negative sign)
Find the characteristics and graph: −12( y + 2) = x2 .
Vertex Do the opposite of the numbers y=
(point) with x and y.
Point on Pick a value right next to the
Parabola vertex and plug into the equation.
Mirror this point
Focus Go directly below the vertex a
(point) length of “p.”
Directrix A horizontal line that is “p”
(line) directly above the vertex.
Parabolas that Open Right
Form : 4 p(x − h) = ( y − k)2 (note “y” part is squared)
Find the characteristics and graph: 4(x + 4) = ( y −1)2 .
Vertex Do the opposite of the numbers x=
(point) with x and y.
Point on Pick a value right next to the
Parabola vertex and plug into the equation.
Mirror this point.
Focus Go directly right of the vertex a
(point) length of “p.”
Directrix A vertical line that is “p” directly
(line) left the vertex.
Parabolas that Open Left
Form : −4 p(x − h) = ( y − k)2 (note the added negative sign)
Find the characteristics and graph: −16(x −1) = ( y − 2)2 .
Vertex Do the opposite of the numbers x=
(point) with x and y.
Point on Pick a value right next to the
Parabola vertex and plug into the equation.
Mirror this point.
Focus Go directly left of the vertex a
(point) length of “p.”
Directrix A vertical line that is “p” directly
(line) right the vertex.