The quadratic function given is:

$f(x) = 8x^2 - 16x - 15$

To find the zeros of the quadratic function, we need to solve the equation $f(x) = 0$, or:

$8x^2 - 16x - 15 = 0$

We can solve this quadratic equation using the quadratic formula:

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

Here, $a = 8$, $b = -16$, and $c = -15$. Let’s plug these values into the quadratic formula.

$x = \frac{-(-16) \pm \sqrt{(-16)^2 - 4(8)(-15)}}{2(8)}$

I will now calculate the solution.The zeros of the quadratic function $f(x) = 8x^2 - 16x - 15$ are approximately:

$x_1 = 2.70 \quad \text{and} \quad x_2 = -0.70$

These are the points where the quadratic function intersects the x-axis.

Would you like more details, or do you have any questions?

Here are five related questions to explore further:

1. How can you factor quadratic equations without using the quadratic formula?
2. What is the significance of the discriminant in the quadratic formula?
3. How can you verify the zeros of a quadratic function graphically?
4. How does the quadratic formula handle complex roots?
5. How do you find the vertex of a quadratic function?

Tip: When solving quadratic equations, always check the discriminant ($b^2 - 4ac$) first, as it tells you whether the roots are real or complex.