find equation for a cubic that goes thru (2,3) and (1,0) and is tangent to (-2,0)?
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The general equation for a cubic is
f(x) = ax^3 + bx^2 + cx + d
Plugging in the values you have, you can get three equations. You have four unknowns, so you need one more equation. The additional piece of information you have is that (-2, 0) is a local min or max. Since I don’t know what level you’re at, I’m not sure what to suggest at this point. If you’re in calculus, then take the first derivative of the function and look for critical points – that’ll give you your fourth equation. If you’re in precalc or algebra 2, then realize that you’re being told that (-2, 0) is an even root and work from there. If you’re below that level, I have no idea how you’ll do this.
Hope this helps.
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