### Quadratic equations: Drawing parabolas

### Intersection of parabolas with the axes

The intersection points of a parabola with the #x#-axis are the points along the graph where #y=0#.

To find the #x# coordinates of these points, equate the formula of the parabola to #0# and solve for #x#:

\[ax^2+bx+c=0\]

This can be done by *factorization*, *completing the square, *or using the *quadratic formula*.

A parabola can have two, one, or no intersections with the #x#-axis.

The intersection point of a parabola with the #y#-axis is the point along the graph where #x=0#.

A parabola always has a *single *point of intersection with the #y#-axis.

To find the #y# coordinate of this point, substitute #0# for #x# in the formula of the parabola.

A parabola described by #y=\blue a x^2+\green b x +\purple c# intersects the #y#-axis at the point #\rv{0,\purple c}#.

The intersection point with the #y#-axis is equal to the value of the constant in the quadratic function: #0#. Hence, the coordinates of the intersection point with the #y#-axis are: #\rv{0,0}#.

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