Question

task one: Erika’s equations

1. The point (1, 5) is on the curve: y = ax2 + bx + c. This point gives the linear equation: 5 = a + b + c.

A second point on the curve, (2, 10) gives the linear equation 10=4a+2b+c

A student called Erika thinks that the point (2, 19) is also on the 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 third point should be (3, 19) not (2, 19) as in question 1 above.

• Rewrite the third equation and solve the new system of three linear equations.

• Write down the quadratic function.

3. Suppose that the third point is written as (3, t). Find all values for t that will change the quadratic function y = ax2 + bx + c into a linear function.

Answer 1

we are given

First equation:

Second equation:

(a)

we have

point is (2,19)

so, x=2 and y=19

so, this equation is :

(b)

so, we got system of equations as

now, we can solve for a , b and c

We can see that last two equations are same of left side but not right side

It can not be possible

Hence,

no solution exist......Answer

(2)

we have point (3,19)

so, x=3 and y=19

so, this equation is :

(i)

so, we get system of equations as

now, we can solve for a , b and c

we get

(ii)

we can use formula

we can plug values

.........Answer

(3)

we can plug x=3 and y=t

and find t

..........Answer