Key Characteristics
The graph of a quadratic function.
What is a parabola?
This form of a quadratic function tells whether the parabola opens up or down and the x-intercepts.
What is factored/intercept form?
The standard form equation.
What is ax^2 + bx + c?
The equation for factored form.
What is a (x-r1) (x-r2)?
The equation for vertex form.
What is a (x-h)^2 +k?
The sign on this value tells whether the quadratic function opens up or down.
What is the a?
This form of quadratic tells you whether the parabola opens up or down and the y-intercept.
What is standard form?
The y intercept
f(x) = 3x^2 + 2x + 3
What is (0,3)?
Identify the zeros in the following function
f(x) = (x - 3) (x + 4)
What is (3,0) and (-4,0)?
The vertex of a parabola represented by the equation f(x) = −2(x − 4)^2 − 7
What is (4, -7)?
In this form, you can identify the vertex, y-intercept, and whether the parabola opens up or down.
What is the vertex form?
The line that runs through the vertex and divides the parabola in half.
What is the axis of symmetry?
In standard form, "a" cannot be equal to this number.
The equation to find the axis of symmetry.
What is r1+r2/ 2?
The way this function transforms.
-3 (x-2) ^2 + 6
What is to the right 2 units and up 6 units.
In standard form, this letter identifies the y-intercept.
What is c?
These two characteristics provide a range for how the parabola increases and decreases.
What is an interval of increase and decrease?
The equation to find the axis of symmetry in standard form.
What is -b/2a ?
The y value of the vertex in factored form can be found by doing this.
What is plugging in the axis of symmetry into the function and solving?
The h and k value represent this.
What is the vertex?
Represents the highest or lowest point on the graph.
What is the absolute maximum or minimum?
These two characteristics identify all solutions that would make the quadratic function true for all x and y values.
What is the domain and range?
The value of a in this function is called the
f(x) = 4x^2 + 6x + 2
What is the leading coefficient?
The zeros, how the parabola opens up, and the vertex
-(x + 5) (x + 3)
What is (-5,0) (-3,0)
Opens Downward
Vertex (-4,1)
The transformation of each value in the function.
g(x)= A f( B (x + C)) +D
What is
A- stretches or compresses vertically
B- stretches or compresses horizontally
C- horizontally translates
D- vertically translates