Question

The axis of symmetry for the graph of the function f(x)=3x2+bx+4 is x equals three-halves. What is the value of b?

−18
−9
9
18

Answer 1

The axis of symmetry for a quadratic function of the form \( f(x) = ax^2 + bx + c \) can be found using the formula:

\[
x = -\frac{b}{2a}
\]

Here, we know that the axis of symmetry is \( x = \frac{3}{2} \) and the coefficient \( a = 3 \). We can substitute these values into the formula to find \( b \):

\[
\frac{3}{2} = -\frac{b}{2 \cdot 3}
\]

This simplifies to:

\[
\frac{3}{2} = -\frac{b}{6}
\]

Next, we can solve for \( b \) by multiplying both sides by -6:

\[
-6 \cdot \frac{3}{2} = b
\]

Calculating the left-hand side:

\[
-6 \cdot \frac{3}{2} = -9
\]

So, \( b = -9 \).

Thus, the value of \( b \) is \( \boxed{-9} \).