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Warm Up. Graphing Quadratic Functions. Graphing Quadratic Functions. Brainstorm everything you know about a quadratic function. THE GRAPH OF A QUADRATIC FUNCTION. The parabola opens up if a>0 and opens down if a<0. y = x 2.

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Warm up

Warm Up


Graphing quadratic functions

Graphing Quadratic Functions


Graphing quadratic functions1

Graphing Quadratic Functions

Brainstorm everything you know about a quadratic function.


The graph of a quadratic function

THE GRAPH OF A QUADRATIC FUNCTION

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

y = x2

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

vertex

y = -x2

Axis of symmetry


Standard form

STANDARD FORM

Graph y = 2x2 -8x +6

Solution: The coefficients for this function

Since 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)+6

y = -2

(2,-2).


Graph

GRAPH

VERTEX:

AXIS OF SYMMETRY:

Y INTERCEPT:


Vertex form of quadratic equation

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

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

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

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

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


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