Question

Find the quadratic polynomial whose graph goes through the points (-1,4), (0,5), (2,25)

Answer 1

we know it looks like
\[ax^2+bx+5\] since \((0,5)\) is on the graph
now you need \(a\) and \(b\)

Answer 2

since \((-1,4)\) is on the graph , you know
\[a(-1)^2+b(-1)+5=4\] or
\[a-b=-1\]

Answer 3

then the point \((2,25)\) tells you
\[a(2)^2+b(2)+5=25\] or
\[4a+2b=20\]
solve the system
\[a-b=-1\]\[4a+2b=20\] for \(a\) and \(b\)

Answer 4

double the first one and add it to the second
\[2a-2b=-2\]\[4a+2b=20\]
\[6a=18\implies a=3\]

Answer 5

and b=4?

Answer 6

\[12+2b=20\]
\[2b=8\implies b=4\] yes you are right

Answer 7

thanks!