Maths Investigative Work (2)

1)Construct a quadratic curve of the form as follow:

ax^2 + bx + c = 0

Use appropriate values of a, b, c. State also the quadratic equation that you are using in your solution.

Answer:
3x^2 + 20x + 25


2)Contruct a tangent to the curve stated above any point.

State the equation of the tangent line in your solution.(Hint: Observe the left side panel of the Geogebra)

Answer:


3) (i) How many points of contact are there between the tangent line and the curve?

(ii) State the coordinate, (x,y) of point of contact between tangent line and the curve.

Answer:
3i) One
3ii) (-1.88,-2)

(4)It is possible to have one more than 1 point of contact between the tangent line and the curve?

If yes, state your reason and show an example.

If no, state your reason

Answer:

No, a tangent only touches one point of the curvel. Refer to the Diagram above.

(5)Presentation of solutions and appropriate use of values.

Answer:

5) Solution: a: 3
b:20
c=25
(3x+5)(x+5)