Quadratic Graphs
What is the name of the line that divides a quadratic function exactly in half so that both sides look identical?
The axis of symmetry
The "c" value in standard form tells you which charateristic of the graph?
y-intercept
The coordinates of the y-intercept/initial value for the quadratic function:
y=-2x2 + 5x - 7
What is (0,-7)?
If the x-value of a point on this parabola is 2, what is the y-value of that same point? Use the following equation: y=3x^2+9x-12
18
When asked to graph a quadratic function. You will need to graph two things: a parabola and...
the axis of symmetry
What is the name of the point on a quadratic function that will be the maximum or minimum of the function?
The vertex
Is the vertex of the quadratic function y = 5x2 + 10x - 2 a maximum or minimum point?
It's a minimum
How do you find the x-intercepts of a quadratic/parabola?
estimate the x value at which the graph crosses the x-axis by lookin at it (where y=0).
The vertex for this quadratic function:
y = x2 - 8x - 3
What is (4, -19)?
what is the domain of every quadratic?
all real numbers or (-infinity, infinity)
How many zeros (x-intercepts) can a quadratic function have? List all possibilities.
1,2 or none
How does the "h" value of the vertex form equation transform the function?
Translates/Shifts Horizontally
How do you find a y-intercept for a quadratic/parabola?
Find the coordinates of the y-intercept for the quadratic function:
y=3x2 + 2x - 1
Y-intercept (0, -1)
For a quadratic/parabola that opens down, what will the range of the function be?
(-infinity, vertex y-value)
What is the standard form of a quadratic equation?
y = ax2 + bx + c
What does a negative "a" value do to a parabola?
Reflects the parabola across the x-axis/ makes the parabola open down.
Find the vertex for the quadratic function:
y = x2 + 10x + 6
What is (-5, -19)
If a quadratic/parabola is opening down, will the vertex be a maximum or minimum?
maximum
For a quadratic/parabola that opens up, what will the range of the function be?
(y-value of the vertex, infinity)
What is the vertex form of a quadratic equation? What are the coordinates of the vertex?
y = a(x - h)2 + k and the vertex is (h,k) or
(what is subtracted from x, and what is added on the end)
How does the "k" value of the vertex form equation transform the function?
it moves or translates the vertex/entire parabola up and down
The coordinates of the vertex for this quadratic function:
y = x2 - 4x + 8
What is (2, 4)?
if the vertex is a maximum and is below the x-axis. or if the vertex is a minimum and above the x-axis.
Describe how this graph is different from y = x2. Include direction of opening, skinny, wide, and how it moves(left, right, up, down).
y = -(x+2)2 + 3
opening down
same width
translated left 2
translated up 3