A quadratic function that fits the points (0,5) (2,3) (4,9)

Step-by-step explanation:

y=ax^2+bx+c we are given point (0,5) so if x=0, y=c, so c=5. We have two other points

(2,3)(4,9) which gives us

4a+2b+5=3 and 16a+4b+5=9

Subtracting twice the first from the second

16a+4b+5-8a-4b-10=9-6

8a-5=3

8a=8, so a=1, so using 4a+2b+5=3 we get

4(1)+2b+5=3

2b+9=3

2b=-6

b=-3 so our quadratic is

y=x^2-3x+5