https://file.aiquickdraw.com/mathbot/file/1726005034795ph3fgpip.jpg

To find the vertex of the quadratic function \( f(x) = 4x^2 - 16x + 10 \), we can use the vertex formula. 

For a quadratic function in the form \( f(x) = ax^2 + bx + c \), the x-coordinate of the vertex is given by:

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

Here, the coefficients are:
- \( a = 4 \)
- \( b = -16 \)
- \( c = 10 \)

Let's calculate the x-coordinate of the vertex:

\[
x = -\frac{-16}{2 \times 4} = \frac{16}{8} = 2
\]

Now that we have the x-coordinate, we can substitute it back into the function to find the y-coordinate:

\[
f(2) = 4(2)^2 - 16(2) + 10 = 4(4) - 32 + 10 = 16 - 32 + 10 = -6
\]

So, the vertex of the function \( f(x) = 4x^2 - 16x + 10 \) is at the point \( (2, -6) \).

Do you want more details or have any questions? 

Here are 5 related questions that could help you expand your understanding:

1. How can you determine if the vertex is a maximum or minimum point?
2. How would you complete the square for the quadratic function to find the vertex?
3. What does the graph of \( f(x) = 4x^2 - 16x + 10 \) look like?
4. Can you find the roots of the quadratic function using the vertex form?
5. How does changing the coefficient \( a \) affect the position of the vertex?

**Tip:** The vertex form of a quadratic equation is another useful method for finding the vertex directly. The vertex form is \( f(x) = a(x-h)^2 + k \), where \( (h, k) \) is the vertex.

Find the vertex of the quadratic function f(x) = 4x^2 - 16x + 10.

This guide shows how to find the vertex of the quadratic function f(x) = 4x^2 - 16x + 10 using the vertex formula. Suitable for students in Grades 9-11, the solution covers core algebraic concepts and steps to find the vertex (2, -6).

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation