finding the equation of a cubic function with 2 points

Question

A cubic function is in the form $y=kx^3+c$. Find the equation if it passes through $(0,5)$ and $(2,-3)$.

I’m not sure how i would work this out algebraically or if i even can without graphing.

Answer 1

c=5,k=-1 Just plug in the values of the first point and the second point, solve the first equation for c, solve the second equation for k(with c=5). And you have your function y = - x³ + 5

Answer 2

It passes through $(0,5)$, right? The first number in that pair is the value of $x$ and the corresponding value of $y$. So when $x=0$, $y=5$. Substitute it into your equation: $5=0+c$. It must hold since it passes through $(0,5)$. Hence you can conclude that $c=5$. Proceed further for the other point yourself.