So, we are given the y intercept, and since we know c is the same as the y value of the y intercept, we know that c=15.
From there we can pick any two of the points given to us to find our a and b.
Let's use (4,17) and (8,23) becase they are whole numbers.
[tex] 17=16a+4b+15\\
23=64a+8b+15 \implies \\
2=16a+4b\\
8=64a+8b \implies\\
8=64+16b \\
8=64+8b \implies \\
0=8b \implies\\
b=0
[/tex]
So, with b=0, we can plug it back into the first equation to get:[tex] 17=16a+4b+15 \implies\\
2=16a \implies\\
a=\frac{1}{8} [/tex]
So our quadratic is [tex] \frac{1}{8}x^2+15 [/tex]
