QUADRATICS
MAKE SENSE
Vertex Form - Key Features
Parabolas are the graph of a quadratic relation and they have important features:
-they can open up or down
-have 2 x-intercepts
-a vertex
-an axis of symmetry
-an optimal value
Vertex
The vertex is the changing point on a graph - it is where the parabola is at its maximum or minimum value. (Shown on the graph above)
It is labeled as (h,k). The h value of the vertex is determined by the axis of symmetry and the k value is determined by the optimal value.
Optimal Value
The optimal value is the maximum or minimum value, and the k value of the vertex.
It is labelled as y=k.
It also determines the direction of opening of the parabola - if the optimal value is minimum, the parabola opens UP. If the optimal value is maximum, the parabola opens DOWN. You can also use this tip vise-versa by finding the optimal value from the direction of opening.
Axis of Symmetry
The axis of symmetry - can written as A.O.S - divides the parabola in half. It is also the h value of the vertex.
It is labeled as x=h.
X&Y Intercepts
An x-intercept is the point on a graph where the line passes through the x-axis. In the case of a parabola, there are 2 x-intercepts, which means that the line passes through the x-axis in 2 different places. X-intercepts can also be called zeroes.
It is labelled as (x,0), and can be found by having y equal zero, and solving for x.
A y-intercept is similar but it is the point on a graph where the line passes through the y-axis. A parabola only has 1 y-intercept.
It is labelled as (0,y) and can be found by having x=0 and solving for y.