Question

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

(-2, 5)
(-2, 5)

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

(0, 8)
(0, 8)

(3, -10)

Answer 1

To find the vertex of the parabola given by the equation \( y = 2x^2 - 12x + 8 \), we can use the formula for the vertex of a parabola in the form \( y = ax^2 + bx + c \) where the x-coordinate of the vertex is given by:

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

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

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

Next, we substitute \( x = 3 \) back into the original equation to find the y-coordinate of the vertex:

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

Therefore, the vertex of the parabola is at the point \( (3, -10) \).

The correct response is:
**(3, -10)**