Questions: Consider the following function. g(x)=x^2+6 x+5

Solution Steps

To find the vertex of a quadratic function in the form \( g(x) = ax^2 + bx + c \), we can use the vertex formula \( x = -\frac{b}{2a} \). Once we have the x-coordinate of the vertex, we can substitute it back into the function to find the y-coordinate.

The given quadratic function is \( g(x) = x^2 + 6x + 5 \). Here, the coefficients are:

• \( a = 1 \)
• \( b = 6 \)
• \( c = 5 \)

Using the vertex formula \( x = -\frac{b}{2a} \): \[ x = -\frac{6}{2 \cdot 1} = -3.0 \]

Substituting \( x = -3.0 \) back into the function to find the y-coordinate: \[ y = g(-3.0) = (-3.0)^2 + 6(-3.0) + 5 = 9 - 18 + 5 = -4.0 \]

Final Answer