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Standard Form

100

What is standard form for a quadratic function?

y = ax² + bx + c

200

What is the axis of symmetry for a quadratic function written in standard form y = ax² + bx + c?

x = -b/2a

300

How do you calculate the vertex of a parabola written in standard form?

x = -b/2a. Then plug in x to the function to solve for the y coordinate

400

What is the axis of symmetry of
Y = 2x² + 2x?

Is the vertex a min. or max?

• -b/2a = -2/2(2) = -½

• → x = -½

• Minimum

500

• Which way will the parabola y = 3x² + 2x + 1 open?

• Is the vertex a minimum or maximum?

• “a” value of ax² + bx + c is positive

• → Up

  • Minimum

Vertex Form

100

What is vertex form for a quadratic function?

Y = a(x-h)² + k

200

What is the axis of symmetry for a parabola written in vertex form Y = a(x-h)² + k?

Vertex: (h, k)

300

What is the vertex of a parabola written in vertex form?

(h, k)

400

What is the vertex of a parabola written in vertex form?

(h, k)

500

What is the axis of symmetry of
-(x+1)²+2?

• What is the vertex?

• Is the vertex a min. or max?

• X = h

• → x = -1

• Vertex

  • (h, k)

  • → (-1, 2)

  • Maximum

Graphing

100

• Which way will the parabola y = 3(x-3)² + 1 open?

• Is the vertex a minimum or maximum?

• “a” value of a(x-h)² + k is positive

• → Up

  • Minimum

200

• Which way will the parabola y = -3(x-3)² + 1 open?

  • Is the vertex a min. or max?

• 
  

  • “a” is negative

  • → Down

  • Maximum

300

• How do you use a table of values to graph a parabola?

• Find the vertex and place it in the middle of the table

• Find the next two points on the left and right of the vertex by plugging in x values to the function

• Plot all points and connect them smoothly. Don’t forget to draw your arrows!

400

• What is the domain of this parabola?

• Range?
  

• Domain: the set of all possible x values

• ℝ (all real numbers)

• Range: The set of all possible y values

  • Y ≤ 2

500

Graph y = -2x² - 3x + 3

Geogebra.org/calculator

Vertex -b/2a

Opens down

y-intercept at 2

Transformations

100

What is the equation of the “parent function”

• To make us go to the dentist…

Y = x²

200

What is a transformation?

Change in size or position

300

Write an equation for the transformation from the parent function:

Reflected over the x-axis, then translated 3 units down

y = -x² -3

400

Write an equation for the transformation from the parent function:

Vertically compressed by a factor of ⅓, then translated 8 units up

1/3 x² + 8

500

Write an equation for the transformation from the parent function:

Vertically stretched by a factor of 2, reflected over the x-axis, then translated 4 units left

y = -2(x+4)²

Misc.

100

• Which way will the parabola y = -3x² + 2x + 1 open?

  • Is the vertex a min. or max?

• 
  

  • “a” is negative

  • → Down

  • Maximum

200

Graph y = -(x+2)² + 7

Geogebra.org/calculator

vertex (-2, 7)
opens down

300

Without graphing, describe the transformation from the parent function:

y = (x-2)² + 1

Right 2, up 1

400

Write an equation for the transformation from the parent function:

3 units left, 4 units down

y = (x+3)² + 4

500

Without graphing, describe the transformation from the parent function:

y = -99(x+9)² - 99

Reflected over x-axis

Stretched/narrowed by a factor of 99

Translated Left 9

Translated Down 99