Show:
Vertex
Axis of Symmetry
Opens Up or Down
Graph It
Challenge
100

f(x) = x2 - 4x

What is (2, -4)

100
The formula of finding the axis of symmetry

What is x = -b/2a

100

f(x) = x2 - 4x + 1

What is Opens UP, a = 1 > 0

100

f(x) = (x - 2)2 + 3

Include Key Features: 

A. Vertex 

B. Axis of Symmetry

C. Opens up/ Opens down

What is

A. Vertex: (2, 3)

B. Axis of Symmetry: x = 2

C. Opens up: Min

100

A student says: "The graph of y = -x2 + 4 opens up"

What is the mistake?

It actually opens DOWN because a = -1

200

f(x) = x2 - 6x + 5

What is (3, -4)

200

f(x) = x2 + 8x + 12

What is x = -4

200
f(x) = -x2 + 6x - 2

What is Opens DOWN

200

f(x) = x2 - 4x + 1

A. Vertex 

B. Axis of Symmetry

C. Opens up/ Opens down

What is

A. Vertex: (2, -3)

B. Axis of Symmetry: x = 2

C. Opens up: Min

200

f(x) = (x - 2)2  + 1.

Will the graph eever touch or go below the x-axis?

No because the vertex is (2, 1), so the graph stays above.

300

f(x) = -x2+4x - 5

What is (2, -1)

300

f(x) = -x2 - 4x + 1

What is x = -2

300

f(x) = 3x2 - 5x + 4

What is Opens UP

300

f(x) = (x + 1)2 - 4

Include the Key Features:

A. Vertex:

B. Axis of Symmetry: 

C. Opens up/down

What is

A. Vertex: (-1, -4)

B. Axis of Symmetry: x = -1

C. Opens up: Min

300

Which graph has the same vertex?

A. y = (x - 3)2 + 2

B. y = (x + 3)2 + 2

C. y = ( x - 2)2 + 3

A. y = (x - 3)2 + 2

400

f(x) = 2x2 - 8x + 6

What is (2, -2)

400

f(x) = 2x2 -- 10x + 3

What is 10/4 or 2.5

400

Which function opens down AND is wider than y = x2?

A. f(x) = -x2

B. f(x) = -3x2

C. f(x) = 1/2x2


What is A. f(x) = -x2

400

f(x) = -(x + 1)2 + 2

Include the Key Features:

A. Vertex:

B. Axis of Symmetry: 

C. Opens up/down

What is

A. Vertex: (1, 2)

B. Axis of Symmetry:  x = 1

C. Opens down: Max

400

A graph has:

A. Opens down.

B. Has a vertex (2, 3).

Write one possible equation

f(x) = -(x - 2)2 + 3

f(x) = -2(x - 2)2 +3

f(x) = -3(x - 2)2 +3

f(x) = -1/2(x - 2)2 +3

500

The vertex of a quadratic is: (-3, -4). The equation is: f(x) = 2x2 + bx + c

What is the value of b?

What is b = 12

500

A quadratic has am axis of symmetry: x = -2. One of the terms in the equation is + 4x.

What must the value of "a" be if the equation is in the form: f(x) = ax2 + 4x + c

What is a=1

500

Which graph is narrower AND opens up?

A. f(x) = x2
B. f(x) = 4x2
C. f(x)= -2x​2​​​

What is B. f(x) = 4x2

500

f(x) = -x2 + 4x + 1

Include the Key Features:

A. Vertex:

B. Axis of Symmetry: 

C. Opens up/down

What is

A. Vertex: (2, 5)

B. Axis of Symmetry: x = 2

C. Opens down: Max

500

What is the quadratic formula?