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

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

Click on the "Vertex and Point" button to get the coordinates of your points.

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

, 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 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.

4. Calculate a.

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.

5. Substitute your values for a, h and k into the form below. You can use fraction form m/n for a.

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...