what is the equation in standard form, of a parabola that models the values in the table.
x|-2|0|4 F(x) |-7|3|-73

Question

what is the equation in standard form, of a parabola that models the values in the table. 
x|-2|0|4 F(x) |-7|3|-73

kirbykirby · Answer

You could approach this by either guessing values for the coefficients. Since you have "small" integer values to deal with, this is do-able if you  have some good intuition. 

However, You can approach this more systematically: the equation of the parabola has the form $f(x) = ax^2+bx+c$ , and they give you 3 x-values and 3-f(x) values. Since the parabola has 3 coefficients $a, b, c$, you can find then by doing a system of 3 equations and 3 unknowns. However, you can reduce that to 2 equations and 2 unknowns very quicly by observing that for $x=0$, $f(0)=3$ which implies $c=3$ ... this is because $f(0)=a(0)^2+b(0)+c\
3 = 0 + 0 + c \implies c=3$

So, the rest can be found doing:
$$-7=a(-2)^2+b(-2)+3\
-73=a(4)^2+b(4)+3 $$ which is a system of equations which you can solve for a and b