Key Features of Quadratic Graphs
Vocabulary Terms
Vertex Form
Standard Form
100
In terms of which way this graph opens, one could say...
The graph opens upwards (smiley face).
100
The name given to describe the graph of a quadratic function, which is a curve.
Parabola.
100
How does "k" affect the graph of the General Vertex Form: f(x) = a(x-h)2+k?
*Be sure to tell me both parts, sign and value!*
"k" moves the graph up and down.
The sign of "k" gives us direction, (+) being up, and (-) being down.
The value of "k" gives us how many units up/down the graph is moving.
100
When given a function in Standard Form (ax2+bx+c), plugging in 0 for "x" results in...
The y-intercept. Given as a point (0, y)
200
In terms of which way this graph opens, one could say...
This graphs opens downwards.
200
The highest or lowest point on a quadratic graph, listed as a point: (x, y).
Vertex.
200
How does "h" affect the graph of the General Vertex Form: f(x) = a(x-h)2+k?
*Be sure to tell me both parts, sign and value!*
"h" tells us if the graph is moving left or right.
SIGNS ARE OPPOSITE! Meaning that to move left, you would need a (+) sign, and to move right, you would need a (-) sign.
The value tells us how far left/right.
200
Using Standard Form, you can plug values into _______ to compute the A.O.S. and the x-value of the vertex.
`-b/(2a)`
300
In comparison to the graph of x2, the graph of 7x2 can be described as...
The graph of 7x2 is skinnier than the graph of x2.
300
What is the quadratic parent function? Give me the actual function.
The Quadratic Parent Function is f(x) = x2.
300
Describe how the graph (given in Vertex Form) of each function is related to x2.
Function: k(x) = (x+5)2-6
- Translate down 6 units
- Translate left 5 units
- Opens upwards
- Vertex: (-5,-6)
- A.O.S.: x=-5
300
Given this equation in Standard Form, y=3x2+6x+3, find the y-intercept.
Y-Intercept: (0,3)
400
In comparison to the graph of x2, the graph of .125x2 can be described as...
The graph of .125x2 is wider than the graph of x2.
400
What is the difference between a transformation and a translation in terms of a quadratic graph?
Transformation: change in size of the graph; wider or skinnier
Translation: the graph moves up, down, left, or right
400
Describe how the graph (given in Vertex Form) of each function is related to x2.
Function: g(x) = .25(x-3)2+4
- Translate up four units
- Translate right 3 units
- Opens upwards
- Transformation, making a skinnier graph
- Vertex: (3,4)
- A.O.S.: x=3
400
Given this equation in Standard Form, y=4x2-8x-12, tell me the Vertex and Axis of Symmetry.
Vertex: (1, -16)
A.O.S.: x=1
500
Thinking in general about "ax2", what does the value and sign of "a" tell us?
*Be sure to list the four different features, two dealing with the value, and two dealing with the sign.*
1.) a<1, the graph becomes wider
2.) a>1, the graph becomes skinnier
3.) when a is positive, the graph opens upwards (smiley face)
4.) when a is negative, the graph opens downwards (upsetti-spaghetti)
500
State a definition of "axis of symmetry". Tell me what it is and how you write/describe it.
Axis of Symmetry: a line through a graph so that each side is a mirror image. When the shape is folded in half along the axis of symmetry, the two halves match up.
Describe by: x=...
500
Thinking in general of a complete Vertex Form function [h(x)=a(x-h)2+k], list the 5 different description pieces you can tell from Vertex Form functions.
Use this function: h(x) = -3(x-2)2+5, as a reference.
1. "k", moving up and down
2. "h", moving left and right (OPPOSITE)
3. "a", making the graph wider or skinner, and opening upwards or downwards
4. Vertex
5. Axis of Symmetry
500
Using this Standard Form equation, y=-2x2+8x-6, tell me the Vertex, the Axis of Symmetry, and the Y-Intercept.
Vertex: (2, 2)
A.O.S.: x=2
Y-Intercept: (0,-6)