Hi Mike… can you work through the steps to solve Q 24 from Official Test 9 Section 4? thanks!

Sure thing. Remember that when you have an f(x) defined and then you’re asked about something like f(x+a), you plug that WHOLE thing in parentheses (called the argument) into the original function where x was. Like so:


Once you’ve expanded it, remember that corresponding coefficients in equal polynomials are equal. So because we know the above is equivalent to 5x^2+30x+42, we know that the x terms are equal: 10ax=30x, and that the constant terms are equal 5a^2-3=42.

To get the value of a, let’s solve the equation without an a^2 term, to avoid having to wonder whether we need the positive or negative root (spoiler alert: both are answer choices).


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