5.1GRAPHING QUADRATIC

FUNCTIONSI can graph quadratic functions in standard form.

I can graph quadratic functions in vertex form.

I can graph quadratic functions in intercept form. You NEED graph paper today!

QUADRATIC FUNCTION? We’ve been working with functions in the form y =

mx + b. This was called a linear function because the graph was a straight

line.

A quadratic function is the form: y = ax2 + bx + c

where a ≠ 0 The graph of a quadratic function is:

A parabola

What’s different between a linear function and a quadratic function?

QUADRATIC FUNCTION IN STANDARD FORM Y = AX2 + BX + C

To find the vertex: The x coordinate is

To find the y coordinate, plug x back into the original function

Vertex Can either be the minimum of

the parabola or the maximum of the parabola.

If a is positive… The parabola goes up (like a

cup)

If a is negative… The parabola goes down (like a

frown)

QUADRATIC FUNCTIONY = AX2 + BX + C

Axis of symmetry Parabolas are always symmetric.

Makes a vertical ‘imaginary’ line at the x coordinate of the vertex that cuts the parabola into equal halves.

EXAMPLE 1: GRAPHING A QUADRATIC FUNCTION IN STANDARD

FORM

y = 2x2 – 8x + 6

Vertex:

x = x = x = x = 2

Standard Form: y = ax2 + bx +

ca= 2b= -8c= 6 y = 2(2)2 – 8(2)

+ 6 y = 2(4) – 16 +

6 y = 8 -10 y = -2

(2, -2)

Axis of Symmetry: x = 2

You also need two more points to be able to make the graph.

Choose x = 3 and x = 4 because they are right after the Axis of Symmetry

y = 2(3)2 – 8(3) + 6 y = 2(9) – 24 + 6 y = 18 – 24 + 6 y = 0

(3, 0)

y = 2(4)2 – 8(4) + 6 y = 2(16) – 32 + 6 y = 32 – 32 + 6 y = 6

(4, 6)

Vertex: (2, -2) Axis of

Symmetry: x = 2

Points: (3,0) (4,6)

INDIVIDUAL PRACTICE ON GRAPHING QUADRATICS IN STANDARD FORM

Pg 253 20-25

List the vertex Axis of symmetry At least 2 extra

points

You have 15 minutes to work on this section of problems.

I will do the next part of notes in 15 minutes.

QUADRATIC FUNCTION IN VERTEX FORM

y = a(x – h)2 + k Vertex:

(h,k) Axis of

Symmetry: x = h

You still also need to find two more points to plot.

EXAMPLE 2: GRAPHING A QUADRATIC FUNCTION IN VERTEX FORM

y = -3(x + 1)2 + 2 Vertex:

(-1,2)

Axis of Symmetry: x = -1

Points: (0,-1) (1,-10)

x = 0

y = -3(0+1)2 + 2 y = -3(1)2 + 2 y = -3(1) + 2 y = -3 + 2 y = -1

x = 1 y = -3(1+1)2 + 2 y = -3(2)2 + 2 y = -3(4) + 2 y = -12 + 2 y = -10

Vertex Form: y = a(x – h)2 +

k

Vertex: (-1,2)

Axis of Symmetry: x = -1

Points: (0,-1) (1,-10)

INDIVIDUAL PRACTICE ON GRAPHING QUADRATICS IN VERTEX FORM

Pg. 253 26-31

List the vertex Axis of symmetry At least 2 extra

points

You have 15 minutes to work on this section of problems.

I will do the next part of notes in 15 minutes.

QUADRATIC FUNCTIONS IN INTERCEPT FORM

y = a(x – p)(x – q)

The x-intercepts are p and q.

The axis of symmetry is halfway between p and q.

The vertex is found by plugging the axis of symmetry back in to the function and solve for y.

EXAMPLE 3: GRAPHING QUADRATICS IN INTERCEPT FORM y = -(x + 2)(x - 4) X-intercepts:

-2 and 4 Axis of symmetry:

x = 1 Vertex:

(1,9)

x = 1 y = -(1+2)(1-4) y = -(3)(-3) y = -(-9) y = 9

Intercept Form: y = a(x – p)(x –

q)

X-intercepts: -2 and 4

Axis of symmetry: x = 1

Vertex: (1,9)

INDIVIDUAL PRACTICE ON GRAPHING QUADRATICS IN INTERCEPT FORM

Pg. 254 32-37

List the vertex Axis of

symmetry Intercepts