Quadratic Fun 1

Construct a Quadratic - vertex & a

If the vertex (h,k) and the coefficient a of x^2 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 point.

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

2. Click on the "Vertex" button.

3. Click on the "Draw Parabola" button.

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

4. Change the coefficient a!

How? What does a do?

Click on

icon and click and drag the slider left and right.

The coefficient a controls the size and the direction of the quadratic. What doesn't it control?

5. 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.

6. Change the coefficient a again.

What doesn't move?

The vertex doesn't move - nor does the axis of symmetry.

7. Move the vertex A.

How? What controls the axis of symmetry?

Click on

icon and click and drag the point A.

The vertex A determines the axis of symmetry.
More precisely the x-coordinate of the vertex!

Use the Move Drawing Pad or Zoom out and click and drag the blue point to the left of the slider to move your parabola anywhere on the graph!

Okay - boring bit coming up.

IMPORTANT: Click on the "Vertex" button!

Vertex: (x, y) \quad

8. Write the equation of the parabola.

• Substitute your values for a, h and k into the form below and click on the Graph your Function button .

If the parabolas match then your answer is correct!