Question

Create the quadratic function that contains the points (0, -2), (1, 0) and (3, 10). Show all of your work for full credit.

Answer 1

If it's a quadratic we know that it must look like $y=ax^2+bx+c$ for some numbers a,b and c. To find these numbers we use the coordinates.

(0,-2) lies on the curve so when x=0, y=-2

$y=ax^2+bx+c \Rightarrow -2=a(0^2)+b(0)+c \Rightarrow -2 = c$

(so that solves one of them)

Next (1,0) lies on the curve so when x=1, y=0

$y=ax^2+bx-2 \Rightarrow 0=a(1^2)+b(1) -2 \Rightarrow a+b-2=0 \Rightarrow a+b=2$

Finally (3,10) lies on the curve so when x=3, y=10

$y=ax^2+bx-2 \Rightarrow 10 = a(3^2)+b(3)-2 \Rightarrow 9a+3b-2=10 \Rightarrow 9a+3b=12 \Rightarrow 3a+b=4$

So then we have to solve the simultaneous equations to get a and b

$a+b=2 \\ 3a+b=4$

These equations have solutions a=1 and b=1 and so we have a=1, b=1, c=-2.

Therefore the equation of the quadratic is $y=x^2+x-2$