A Quadratic Function Can Be Written in the Form

A quadratic function can be written in the form

y = ax2 + bx + c.

The graph is a smooth curve called a parabola.

Directions for Graphing a Parabola

 Find the coordinates of the vertex A quadratic function can be  Decide whether the graph opens written in the form up or down y = ax2 + bx + c.  Find the y-intercept

 Reflect that point over the axis of symmetry The graph is a smooth curve

 Graph one other set of points by called a parabola. following the general pattern or plugging in values Directions for Graphing a Parabola

 Find the coordinates of the vertex

 Decide whether the graph opens up or down

 Find the y-intercept  Reflect that point over the axis of  This value is the y-coordinate of symmetry the vertex (the y value tells how high or low the parabola goes)  Graph one other set of points by following the general pattern or plugging in values Standard Form

y = ax2 + bx + c

vertex (, ? )

y-intercept (0, c)

Vertex Form

y = a(x - h)2 + k

vertex (h, k)

y-intercept (0, ?)

In general Intercept Form

 If a > 0 the graph opens up, if y = a(x – p)(x – q) a < 0 the graph opens down x-intercepts (p, 0) and (q,0)  The larger the absolute value of a, the narrower the graph vertex ( , ?) (this is half-way between p and q)

 Each parabola has either a y-intercept (0, ?) maximum or a minimum value In general Intercept Form

 If a > 0 the graph opens up, if y = a(x – p)(x – q) a < 0 the graph opens down x-intercepts (p, 0) and (q,0)  The larger the absolute value of vertex ( , ?) a, the narrower the graph (this is half-way between p and q)

y-intercept (0, ?)  Each parabola has either a maximum or a minimum value

 This value is the y-coordinate of the vertex (the y value tells how high or low the parabola goes)

Standard Form