Key terms for the unit
Vertex- The minimum or the maximum value on a graph. It is a point where the graph changes direction. It is written as (x,y) where "x" is the co-ordinate on the x-axis, and "y" is the cordinate on the y-axis.
Minimum/maximum value- Highest or lowest value that the graph reaches. It is also known as the optimal value. It is written in the form y=__ where "y" is the highest or the lowest value on the y-axis.
Axis of symmetry- Vertical line that splits the parabola down the middle. It is written in the form of x=___ where "x" is the x-value where the parabola slpits into half.
Y-intercept- the point where the graph crosses the y-axis. It is written in the form of (0,y) where x=0 because it is crossing the y-axis, and on the y-axis, the value of x is always 0. It also includes the "y" value which is value of "y" when the parabola meets the y-axis.
X-intercept- the point where the graph crosses the x-axis. It is written in the form of (x,0) where "y" is 0 because it is crossing the x-axis, and on the x-axis the value of "y" is always 0. It also includes the "x" value which is the value of "x" when the parabola crosses the x-axis.
Zeros- the x-value which makes the equation equal to zero. It is written in the form x=___ where "x" is the value that results in the equation being equal to zero, when it is plugged in the eqaution.
Useful site for more information-http://www.sparknotes.com/math/algebra1/quadratics/terms.html
The "v" is the vertex of the parabola.
Diagram for the
optimal value
Note: Do not think that vertex and the optimal value are the same thing because vertex is the highest or the lowest point, however, optimal value is highest or the lowest "y" value.
It is also the "x" co-ordinate of the vertex. The x-value where the parabola can be spilt in half, which in this case is 3.
Diagram showing the point where the parabola crosses the y-axis (y-intercept).
Diagram showing the points where the parabola crosses the x-axis (x-intercepts).
This image shows the zeros
of a parabola, which in this
case are -1 and 3
Note: The zeros are the same as the x-intercepts, however, x-intercept is a point (x,0), whereas zero is the value of "x" (x=___).