Question

Write a quadratic function whose graph has x intercepts of 7 and 10 and passes through (2,4) what is the value of Y

Answer 1

A quadratic function with x-intercepts 7 and 10 has the form (because when x = 10 , y = 0 and x = 7, y = 0)

`y=c(x-10)(x-7)`

where c is a constant hitherto unknown.

We are told that the quadratic function passes through (2, 4) meaning when x = 2 then y = 4. Putting these values into the above equation gives us

`4=c(2-10)(2-7)`

`\rightarrow4=40c`
`\therefore c=0.1`

Hence, the final form of our quadratic equation is

`y=0.1(x-10)(x-7)`

which is our answer.