Question
What is the vertex of y=x2+6x+13
?(1 point)
Responses
(0, 13)
(0, 13)
(3, 40)
(3, 40)
(-3, 4)
(-3, 4)
(1, 20)
(1, 20)
?(1 point)
Responses
(0, 13)
(0, 13)
(3, 40)
(3, 40)
(-3, 4)
(-3, 4)
(1, 20)
(1, 20)
Answers
GPT-4o mini
To find the vertex of the quadratic function \( y = x^2 + 6x + 13 \), we can use the vertex formula. For a quadratic equation in the form \( y = ax^2 + bx + c \), the x-coordinate of the vertex is given by:
\[
x = -\frac{b}{2a}
\]
In your equation, \( a = 1 \) and \( b = 6 \). Plugging in these values:
\[
x = -\frac{6}{2 \cdot 1} = -\frac{6}{2} = -3
\]
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 is at the point \((-3, 4)\).
The correct response is:
**(-3, 4)**.
\[
x = -\frac{b}{2a}
\]
In your equation, \( a = 1 \) and \( b = 6 \). Plugging in these values:
\[
x = -\frac{6}{2 \cdot 1} = -\frac{6}{2} = -3
\]
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 is at the point \((-3, 4)\).
The correct response is:
**(-3, 4)**.