Question

the graph of the function f(x) = 2x² - bx - 6 is shown. what is the value of b? explain.
the
of the parabola is(are)
the formula for this(these) point(s) can be used to determine that b =
(simplify your answer.)

Explanation:

Step1: Identify x-intercepts from graph

From the graph, the parabola intersects the x - axis at \(x = 3\) and \(x=- 1\) (assuming the grid and the shape of the parabola, we can find the roots). So the roots of the quadratic equation \(2x^{2}-bx - 6=0\) are \(x_1 = 3\) and \(x_2=-1\).

Step2: Use sum of roots formula

For a quadratic equation \(ax^{2}+bx + c = 0\) (here our equation is \(2x^{2}-bx - 6 = 0\), so \(a = 2\), \(c=-6\) and the coefficient of \(x\) is \(-b\)), the sum of roots \(x_1 + x_2=-\frac{\text{coefficient of }x}{a}\).

The sum of roots \(x_1 + x_2=3+( - 1)=2\). And from the formula, \(x_1 + x_2=-\frac{-b}{2}=\frac{b}{2}\).

Step3: Solve for b

Set \(\frac{b}{2}=2\). Multiply both sides by 2: \(b = 4\).

Answer:

\(b = 4\)