Question 240777
If {{{f(x) = 3x^2-8x}}}, then {{{f(a) = 3a^2 -8a}}}. And if f(a) = -5 then {{{-5 = 3a^2 -8a}}}.<br>
Now we just solve for a. Since this is a quadratic equation we will
1) Get one side equal to zero (by adding 5 to each side):
{{{0 = 3a^2 - 8a +5}}}
2) Factor (and use the Zero Product Property) or use the Quadratic Formula.
{{{0 = (3a - 5)(a-1)}}}
By the Zero Product Property, this or any product can be zero only if one (or more) of the factors is zero. So
{{{3a - 5 = 0}}} or {{{a-1 = 0}}}
Solving these two equations we get:
{{{3a = 5}}} or {{{a = 1}}}
{{{a = 5/3}}} of {{{a = 1}}} (You will get these same answers if you use the Quadratic formula correctly.)