Quadratics Fun - 2
Construct a Quadratic - vertex & point

If the vertex (h,k) and one other point (x,y) on the graph of a parabola are known, you can write the equation of the parabola in vertex form.

   \color{red}{ f(x)=a(x-h)^2+k}


1. Draw a vertex and point.

• Select Point and then click in the pad to get your vertex A.

• Click again in the pad to get your point B.


   Vertex: (h, k) \quad Point: (x, y)


Now - let's have some fun before calculating Smiley.


2. Draw the axis of symmetry through the vertex.

Thinking...  How?

   Axis of symmetry goes through vertex and is perpendicular to x-axis.
   Select Perp, click on A and then on the x-axis.

3. Draw the point C on the parabola symmetric to B.

Thinking...  How?

   Need to mirror B around axis of symmetry.
   Select Mirror_Line, click on B and then on line of symmetry.

Use the Move Drawing Pad or Zoom out until you see all three points!

Now - if we calculate correctly - our parabola will go through these three points A, B and C.


Thinking...  How?

   Substitute values for: h,k,x and f(x) into top formula.
    (h,k) are the coordinates of the vertex A and (x,f(x)) are the coordinates of any point on the parabola - use B.

f(x) = (x - )^2 +

If the parabola goes through A, B and C then your answer is correct!



Problems?   Thinking 1...  &  Thinking 2...

   Did you remember to square (x-h)?
   Check your signs again...

Scroll down!


                    
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      RF & LFS , Created with GeoGebra