If a function has constant second differences, then it is a quadratic function.
y=2x^2-5
Practice makes perfect
If a function has constant second differences but not constant first differences, then we can say that it is a quadratic function. Since this function has a y-intercept other than zero, it should have the form below.
y= ax^2+c
Here, c is the y-intercept. We know the function has a y-intercept of - 5, c=- 5.
y=ax^2+c
⇓
y=ax^2+(- 5)
Now, we can use the given point ( 2, 3) to find the value of a.
