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!

Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and activated. (click here to install Java now)

      RF & LFS , Created with GeoGebra