Warm Up

Graphing Quadratic Functions

Graphing Quadratic Functions

Brainstorm everything you know about a quadratic function.

THE GRAPH OF A QUADRATIC FUNCTION

vertex

Axis of symmetry

y = x2

y = -x2

The parabola opens up if a>0 and opens down if a<0

The parabola is wider than the graph of y = x2 if |a| < 1 and narrower than the graph of y = x2 if |a| > 1.

STANDARD FORM

Graph y = 2x2 -8x +6

Solution: The coefficients for this functionSince a>0, the parabola opens up.

The x-coordinate is: x = -b/2a

The y-coordinate is:

The vertex is

a = 2, b = -8, c = 6.

x = -(-8)/2(2) x = 2

y = 2(2)2-8(2)+6y = -2

(2,-2).

GRAPH

VERTEX:

AXIS OF SYMMETRY:

Y INTERCEPT:

VERTEX FORM OF QUADRATIC EQUATION

y = a(x - h)2 + k

The vertex is (h,k).

The axis of symmetry is x = h.

GRAPHING A QUADRATIC FUNCTION IN VERTEX FORM

Example y = -1/2(x + 3)2 + 4

VERTEX:

AXIS OF SYMMETRY:

Y INTERCEPT:

INTERCEPT FORM OF QUADRATIC EQUATION

y = a(x - p)(x - q)

The x intercepts are p and q.

The axis of symmetry is halfway between (p,0) and (q,0).

GRAPHING A QUADRATIC FUNCTION IN INTERCEPT FORM

Example y = -(x + 2)(x - 4).

VERTEX:

AXIS OF SYMMETRY:

Y INTERCEPT:

X INTERCEPT:

WRITING THE QUADRATIC EQUATION IN STANDARD FORM

(1). y = -(x + 4)(x - 9)

(2). y = 3(x -1)2 + 8

-x2 + 5x + 36

3x2 - 6x + 11