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

Using the vertex of the quadratic equation, it is found that the value of b is of -9.

What is the vertex of a quadratic equation?

A quadratic equation is modeled by:

$y = ax^2 + bx + c$

The vertex is given by:

$(x_v, y_v)$

In which:

$x_v = -\frac{b}{2a}$

$y_v = -\frac{b^2 - 4ac}{4a}$

The axis of symmetry is $x = x_v = -\frac{b}{2a}$.

Considering the coefficient a, we have that:

• If a < 0, the vertex is a maximum point.

• If a > 0, the vertex is a minimum point.

In this problem, we have that the function is defined as follows:

$f(x) = 3x^2 + bx + 4$

We have that $a = 3, x_v = \frac{3}{2}$, hence the value of b is found as follows:

$x = -\frac{b}{2a}$

$\frac{3}{2} = -\frac{b}{6}$

b = -6 x 3/2

b = -9.

More can be learned about the vertex of a quadratic equation at https://brainly.com/question/24737967

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