task one: Erika’s equations
1. The point (1, 5) is on the curve: y = ax2 + bx + c. Thispoint gives the linear equation: 5 = a + b + c.
A second point on the curve, (2, 10) gives the linear equation10=4a+2b+c
A student called Erika thinks that the point (2, 19) is also onthe curve.
a. Use the point (2, 19) to write the third equation.
b. Attempt to solve this system of three linear equations.Explain the meaning of your answer in geometrical terms.
2. Erika realises that she has made an error and that the thirdpoint should be (3, 19) not (2, 19) as in question 1 above.
• Rewrite the third equation and solve the new system of threelinear equations.
• Write down the quadratic function.
3. Suppose that the third point is written as (3, t). Find allvalues for t that will change the quadratic function y = ax2 + bx +c into a linear function.
