Question

What is the vertex of y=2x2−12x+8
?(1 point)
Responses

(0, 8)
(0, 8)

(-3, 62)
(-3, 62)

(3, -10)
(3, -10)

(-2, 5)

Answer 1

To find the vertex of the quadratic function \(y = 2x^2 - 12x + 8\), we can use the vertex formula for a parabola defined by \(y = ax^2 + bx + c\). The x-coordinate of the vertex can be found using the formula:

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

In this equation, \(a = 2\) and \(b = -12\). Plugging in these values, we get:

\[
x = -\frac{-12}{2 \cdot 2} = \frac{12}{4} = 3
\]

Next, we will find the y-coordinate by substituting \(x = 3\) back into the original equation:

\[
y = 2(3)^2 - 12(3) + 8
\]
\[
y = 2(9) - 36 + 8
\]
\[
y = 18 - 36 + 8
\]
\[
y = 18 - 36 + 8 = -10
\]

Thus, the vertex of the parabola is at the point:

\[
(3, -10)
\]

The correct response is:

**(3, -10)**