Standard Form
Vertex Form
Graphing
Transformations
Misc.
100
What is standard form for a quadratic function?
y = ax² + bx + c
100
What is vertex form for a quadratic function?
Y = a(x-h)² + k
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
100
What is the equation of the “parent function”
To make us go to the dentist…
Y = x²
100
Which way will the parabola y = -3x² + 2x + 1 open?
Is the vertex a min. or max?
“a” is negative
→ Down
Maximum
200
What is the axis of symmetry for a quadratic function written in standard form y = ax² + bx + c?
x = -b/2a
200
What is the axis of symmetry for a parabola written in vertex form Y = a(x-h)² + k?
Vertex: (h, k)
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
200
What is a transformation?
Change in size or position
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
300
What is the vertex of a parabola written in vertex form?
(h, k)
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!
300
Write an equation for the transformation from the parent function:
Reflected over the x-axis, then translated 3 units down
y = -x2 -3
300
Without graphing, describe the transformation from the parent function:
y = (x-2)2 + 1
Right 2, up 1
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
400
What is the vertex of a parabola written in vertex form?
(h, k)
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
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
400
Write an equation for the transformation from the parent function:
3 units left, 4 units down
y = (x+3)2 + 4
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
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
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
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