Question
what is the vertex of y=2x^2 - 12x+8
Answers
GPT-4o mini
To find the vertex of the quadratic equation \( y = 2x^2 - 12x + 8 \), we can use the vertex formula for a parabola, which is given by the coordinates:
\[
x = -\frac{b}{2a}
\]
In this equation, \( a = 2 \) and \( b = -12 \).
1. Calculate the \( x \)-coordinate of the vertex:
\[
x = -\frac{-12}{2 \times 2} = \frac{12}{4} = 3
\]
2. Now, to find the \( y \)-coordinate, substitute \( x = 3 \) back into the equation:
\[
y = 2(3)^2 - 12(3) + 8
\]
\[
y = 2(9) - 36 + 8
\]
\[
y = 18 - 36 + 8
\]
\[
y = -10
\]
Thus, the vertex of the parabola described by the equation \( y = 2x^2 - 12x + 8 \) is at the point \( (3, -10) \).
\[
x = -\frac{b}{2a}
\]
In this equation, \( a = 2 \) and \( b = -12 \).
1. Calculate the \( x \)-coordinate of the vertex:
\[
x = -\frac{-12}{2 \times 2} = \frac{12}{4} = 3
\]
2. Now, to find the \( y \)-coordinate, substitute \( x = 3 \) back into the equation:
\[
y = 2(3)^2 - 12(3) + 8
\]
\[
y = 2(9) - 36 + 8
\]
\[
y = 18 - 36 + 8
\]
\[
y = -10
\]
Thus, the vertex of the parabola described by the equation \( y = 2x^2 - 12x + 8 \) is at the point \( (3, -10) \).