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Anaylzing Quadratics

Before we can get anywhere else, we need to know how to tell if we are even dealing with quadratics.Using the "table of values" to figure out if you are looking at a quadratc relationship, is the first step to take.

  • Stubtract the Y values, in order to find the 1st difference. In order to find out if it is a quadratic relation, you subtract the 1st differences.

Overall:

  • a linear relation would have the same FIRST DIFFERENCES

  • a quadratic relation would have the same SECOND DIFFERENCESS

In this case, since the 2nd differnece is all the same, this is a quadratic relation.

Labelling a Parabola

The vertex:

  • it is the maxium/minimum point on the graph

  • it is labelled as a point (X,Y)

 

Maxium or Minium value:

  • it is the optimal vlaue/ highest or lowest point (it is along the horizontal line)

  • it is labelled as the co-ordinate of Y, so y = #

 

Axis of Symmetry:

  • it is the line that divides the parabola in half (it is along the vertical line)

  • it is labelled as the co-ordinate of X, so x = #

 

Y-intercept:

  • it is where the parabola 1st crosses the y-axis

  • it is labelled as a point, where X will always be 0 (0,Y)

  • Note: there will always be a y-intercept because the parabola will always eventually hit the y-axis

 

X-intercept (also known as Zeros or Roots):

  • it is where the parabola 1st crosses the x-axis

  • it is labelled as a point, where Y will always be 0 (X,0)

  • Note: there may not always be a x-intercept because the parabola doesn't always hit the x-axis (there could be one, two or none)

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