+379 The quadratic $\frac43x^2+4x+1$ can be written in the form a(x+b)^2+c, where a,b , and c are constants. What is abc? Give your answer in simplest form.
Thank you!
+9488 =43x2+4x+1
Factor 43 out of all the terms.
=43(x2+3x+34)
Add 94 and subtract 94 to complete the square inside the parenthesees.
=43(x2+3x+94−94+34)
Factor x2+3x+94 as a perfect square trinomial.
=43( (x+32)2−94+34)
Combine −94 and +34
=43( (x+32)2−64)
Distribute the 43
=43(x+32)2−43(64)
And 43(64) = 2
=43(x+32)2−2
Now the expression is in the form a(x + b)2 + c where a, b, and c are constants.
abc = (43)(32)(−2) = (2)(−2) = −4 _
+9488 =43x2+4x+1
Factor 43 out of all the terms.
=43(x2+3x+34)
Add 94 and subtract 94 to complete the square inside the parenthesees.
=43(x2+3x+94−94+34)
Factor x2+3x+94 as a perfect square trinomial.
=43( (x+32)2−94+34)
Combine −94 and +34
=43( (x+32)2−64)
Distribute the 43
=43(x+32)2−43(64)
And 43(64) = 2
=43(x+32)2−2
Now the expression is in the form a(x + b)2 + c where a, b, and c are constants.
abc = (43)(32)(−2) = (2)(−2) = −4 _
