What is the vertex of the quadratic equation y=−2x^2+8x−3 ?(1 point) Responses (0,−3) open paren 0 comma negative 3 close paren (4,−3) open paren 4 comma negative 3 close paren (−2,−27) open paren negative 2 comma negative 27 close paren (2,5)

Answer 1

To find the vertex of the quadratic equation \( y = -2x^2 + 8x - 3 \), we can use the vertex formula:

The x-coordinate of the vertex for a quadratic equation \( y = ax^2 + bx + c \) is given by:

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

In our equation, \( a = -2 \) and \( b = 8 \).

So,

\[ x = -\frac{8}{2 \cdot -2} = -\frac{8}{-4} = 2 \]

Now, we substitute \( x = 2 \) back into the equation to find the y-coordinate of the vertex:

\[ y = -2(2)^2 + 8(2) - 3 \] \[ y = -2(4) + 16 - 3 \] \[ y = -8 + 16 - 3 \] \[ y = 8 - 3 = 5 \]

Thus, the vertex of the quadratic equation is \( (2, 5) \).

So the correct response is:

(2, 5)