Quadratic Function Notes
Basic Terms:
Degree of 2 – means that the highest exponent on the x term will be a 2. No exponents on y.
Parabola – the name of the graph of a Quadratic Function
Standard Form --
Vertex Form –
Factored Form --
x-intercepts – where it intercepts the x-axis. It can have zero (doesn’t touch), one (the vertex only touches), or
two (crosses completely).
Zeros – another name for x-intercepts (because the y = 0 here)
Solutions – yet another name for x-intercepts or zeros. Because this is what we find when we solve.
Root – yet another name used for the zeros, solutions, and x-intercepts.
Quadratic Formula – this is a method of finding the zeros/roots/solutions/x-intercept when “easier” methods
do not work. If the quadratic function is in standard form then:
y-intercept – where it crosses the y-axis. There will only be one. This is the “c” in standard form.
Max & Min – same as before. Max is the “largest” y value, and Min is the “smallest”. If the graph “opens up” it
has a Min, and if it “opens down” it has a Max. In standard form, the “a” will be positive if there is a
Min, and negative if there is a Max.
Domain & Range – the set of x and y values respectively
Vertex – it is the point (ordered pair) on the parabola where the graph “turns” and changes direction. The Max
or Min will be equal to the y value of the vertex. The x value of the vertex is found in standard form
as .
Axis of Symmetry – the “invisible line” going through the vertex that the parabola shows reflection on either
side. Since it is a vertical line, the equation will be x = “the x value of the Vertex”. In standard form
.
Quadratic Function Notes
Basic Terms:
Degree of 2 – means that the highest exponent on the x term will be a 2. No exponents on y.
Parabola – the name of the graph of a Quadratic Function
Standard Form --
Vertex Form –
Factored Form --
x-intercepts – where it intercepts the x-axis. It can have zero (doesn’t touch), one (the vertex only touches), or
two (crosses completely).
Zeros – another name for x-intercepts (because the y = 0 here)
Solutions – yet another name for x-intercepts or zeros. Because this is what we find when we solve.
Root – yet another name used for the zeros, solutions, and x-intercepts.
Quadratic Formula – this is a method of finding the zeros/roots/solutions/x-intercept when “easier” methods
do not work. If the quadratic function is in standard form then:
y-intercept – where it crosses the y-axis. There will only be one. This is the “c” in standard form.
Max & Min – same as before. Max is the “largest” y value, and Min is the “smallest”. If the graph “opens up” it
has a Min, and if it “opens down” it has a Max. In standard form, the “a” will be positive if there is a
Min, and negative if there is a Max.
Domain & Range – the set of x and y values respectively
Vertex – it is the point (ordered pair) on the parabola where the graph “turns” and changes direction. The Max
or Min will be equal to the y value of the vertex. The x value of the vertex is found in standard form
as .
Axis of Symmetry – the “invisible line” going through the vertex that the parabola shows reflection on either
side. Since it is a vertical line, the equation will be x = “the x value of the Vertex”. In standard form
.