Question

What is the vertex of y=x2+6x+13
?(1 point)
Responses

(1, 20)
(1, 20)

(3, 40)
(3, 40)

(-3, 4)
(-3, 4)

(0, 13)

Answer 1

To find the vertex of the quadratic function \( y = x^2 + 6x + 13 \), we can use the vertex formula. The x-coordinate of the vertex for a quadratic in the standard form \( y = ax^2 + bx + c \) is given by \( x = -\frac{b}{2a} \).

Here, \( a = 1 \) and \( b = 6 \).

1. Calculate the x-coordinate of the vertex:
\[
x = -\frac{6}{2(1)} = -\frac{6}{2} = -3
\]

2. Now substitute \( x = -3 \) back into the equation to find the y-coordinate:
\[
y = (-3)^2 + 6(-3) + 13
\]
\[
y = 9 - 18 + 13
\]
\[
y = 4
\]

Thus, the vertex of the quadratic function \( y = x^2 + 6x + 13 \) is \( (-3, 4) \).

So the correct response is:
**(-3, 4)**