Question

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

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

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

(0, 8)
(0, 8)

(3, -10)

Answer 1

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

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

In this case, \( a = 2 \) and \( b = -12 \).

1. Calculate the x-coordinate of the vertex:

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

2. Now, substitute \( x = 3 \) back into the equation to find the y-coordinate:

\[
y = 2(3)^2 - 12(3) + 8
\]

Calculating that gives:

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

Thus, the vertex is at \( (3, -10) \).

So the answer is \( (3, -10) \).