Question

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

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

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

(0, 8)
(0, 8)

(-3, 62)

Answer 1

To find the vertex of the quadratic function \( y = 2x^2 - 12x + 8 \), we can use the vertex formula. The x-coordinate of the vertex can be found using:

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

For the given quadratic, \( a = 2 \) and \( b = -12 \).

Now, calculate:

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

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

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

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

\[
(3, -10)
\]

So the correct response is:

**(3, -10)**