Class Notes: Parabolas Conics – 3
locus definition of a parabola: all points equidistant from a line and a point not on the line
vertex form of a parabola y = a ( x − h ) + k
2
standard form of a parabola y = ax 2 + bx + c
Sketch using transformations:
y = x2
1
2
y = ( x + 2) + 3
2
Convert from standard form to vertex form by completing the square. Then sketch the graph using
transformations.
example 1) y = −2 x 2 + 12 x − 16
2) Write the equation of the parabola with vertex (1, 3) passing through the point (3, 5).
3) Write the equation of the parabola with vertex (3, 1) and having a point on the curve at (1, -3) in vertex and
standard form.
Find the roots of the following equations.
2
y = ( x + 1) − 2
y = x2 + 2 x − 1