Quadratics!!

Equations / Misc

100

What is the quadratic parent function?

f(x)=x^2

200

What is the axis of symmetry in VERTEX form?

x=h

300

What is the axis of symmetry in standard form?

x=-b/2a

400

Explain how you know if the vertex will be a minimum or maximum? 

If there's a negative in front of the x^2 the parabola will open downwards and have a maximum.

If there's a positive in front of the x^2 the parabola will open upwards and have a minimum.  

500

Why do absolute value graphs and quadratic graphs look similar?

A negative number squared is a positive. A negative in absolute value bars is also a positive. Creating the "U" and "V" shape. 

Graph!!

100

y=x^2−4

Shift down 4 

200

y=x^2+6x+8

Axis of symmetry at (-3,-1)

300

y=(x−2)^2+3

Shift right 2, up 3

Vertex: (2,3)

400

y=−2x^2−4x−1

Axis of symmetry (-1,1)

Opens downward 

500

y=−1/2(x−2)^2+1

Vertex: (2,1)

Opens Downwards, Compress 1/2, right 2, up 1

Vertex Form

100

y=(x−3)^2+2

(3,2)

200

y=−2(x+4)^2−1

(-4,-1)

300

y=1/2(x−5)^2−6

(5,-6)

400

y=−3(x+1)^2+4

(-1,4)

500

y=4(x−2)^2−8

(2,-8)

Standard Form

100

y=x^2+6x+5

(-3,-4)

200

y=−x^2+4x+1

(2,5)

300

y=2x^2−8x+7

(2,-1)

400

y=−3x^2−6x+9

(-1,12)

500

y=1/2x^2−4x+2

(4,-6)

Translations

100

y=4(x+2)^2−8

Stretch 4, Left 2, Down 8

200

y=−2(x−5)^2+7

Reflect across the x-axis 

Stretch 2

Right 5

Up 7

300

y=−5/2(x−3)^2−2

Reflect across x-axis

Stretch by 5/2

right 3

down 2

400

y=3/4(x+1)^2+5

Compress 3/4

Left 1

Up 5

500

y=−1/3(x−6)^2+4

Reflect across x-axis

Compress 1/3

Right 6

Up 4