Which is the correct description description of y=4x^2-16x+12?
 
It has max value of -4

It has min value of -4

It has max value of 2

It has min value of 2

The equation \( y = 4x^2 - 16x + 12 \) is a quadratic function. Since the coefficient of \(x^2\) is positive (4), the parabola opens upwards, which means it has a **minimum value**, not a maximum.

To find the minimum value, we first determine the vertex, as the vertex gives us the minimum (or maximum) point for a parabola. The x-coordinate of the vertex can be found using the formula:

\[
x_{\text{vertex}} = \frac{-b}{2a}
\]

For the quadratic equation \( y = ax^2 + bx + c \), we have:
- \( a = 4 \)
- \( b = -16 \)
- \( c = 12 \)

Now, calculate the x-coordinate of the vertex:

\[
x_{\text{vertex}} = \frac{-(-16)}{2(4)} = \frac{16}{8} = 2
\]

Next, substitute \( x = 2 \) back into the equation to find the y-coordinate of the vertex (which will be the minimum value):

\[
y = 4(2)^2 - 16(2) + 12 = 4(4) - 32 + 12 = 16 - 32 + 12 = -4
\]

Thus, the minimum value of the function is \( y = -4 \).

The correct description is:

- **It has a minimum value of -4.**

Would you like more details or explanations? Here are five related questions:

1. How do you determine if a quadratic function has a minimum or maximum?
2. How can you graph the function \( y = 4x^2 - 16x + 12 \) to verify its minimum value?
3. What happens to the graph if the coefficient of \(x^2\) changes from positive to negative?
4. How do you complete the square to find the vertex of a quadratic equation?
5. What are the real-life applications of quadratic functions and their minimum or maximum points?

**Tip:** The vertex form of a quadratic equation, \( y = a(x - h)^2 + k \), makes it easy to see the vertex at \( (h, k) \).

Which is the correct description of y=4x^2-16x+12? It has max value of -4. It has min value of -4. It has max value of 2. It has min value of 2.

Learn how to find the minimum value of the quadratic function y=4x^2-16x+12. This problem demonstrates key concepts such as identifying the vertex of a parabola and applying the vertex formula. Suitable for students in Grades 9-11.

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