https://file.aiquickdraw.com/mathbot/file/17258367614546r5bv68b.jpg

The image shows a math question that requires solving the quadratic function:

\[
f(x) = 2x^2 - 8x - 10 = 0
\]

The answer choices are:

- a. 12
- b. 4
- c. -6
- d. -12

Let me solve this quadratic equation step by step.

First, we start by using the quadratic formula:

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

In this case, the coefficients are:
- \(a = 2\)
- \(b = -8\)
- \(c = -10\)

Let's compute the discriminant (\(b^2 - 4ac\)) and solve for \(x\).The solutions to the quadratic equation \(2x^2 - 8x - 10 = 0\) are:

\[
x_1 = 5 \quad \text{and} \quad x_2 = -1
\]

The discriminant is 144, confirming two real solutions.

Now, from the given choices:
- a. 12
- b. 4
- c. -6
- d. -12

None of these match the solutions of the quadratic equation. It appears that the answer choices might not directly correspond to the roots, but they could relate to another interpretation or part of the problem.

Would you like further clarification or details?

Here are some related questions:
1. How do you interpret the discriminant in quadratic equations?
2. What are the common methods to solve quadratic equations?
3. Can quadratic equations have complex roots? When does this happen?
4. How can the quadratic formula be derived?
5. What is the significance of the axis of symmetry in a quadratic function?

**Tip:** Always check the discriminant (\(b^2 - 4ac\)) before solving to determine if the quadratic has real or complex solutions.

Solve the function f(x) = 2x^2 - 8x - 10 = 0.

Step-by-step solution to the quadratic equation 2x^2 - 8x - 10 = 0 using the quadratic formula. Learn how to compute the discriminant and find real roots. Suitable for students in Grades 9-11.

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