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

Vertex: (h, k) \quad Point: (x, y)

Now - let's have some fun before calculating .

2. Draw the axis of symmetry through the vertex.

Thinking...  How?

Axis of symmetry goes through vertex and is perpendicular to x-axis.
Select , 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 , click on B and then on line of symmetry.

Use the or 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)?