Question

consider the following function.

( g(x) = -x^2 + 4x - 3 )

step 1 of 4: find the vertex.

Explanation:

Step1: Recall vertex formula

For a quadratic function \( g(x) = ax^2 + bx + c \), the x - coordinate of the vertex is given by \( x = -\frac{b}{2a} \). In the function \( g(x)=-x^{2}+4x - 3 \), we have \( a=- 1 \), \( b = 4 \), and \( c=-3 \).

Step2: Calculate x - coordinate

Substitute \( a=-1 \) and \( b = 4 \) into the formula for the x - coordinate of the vertex: \( x=-\frac{4}{2\times(-1)}=-\frac{4}{-2} = 2 \).

Step3: Calculate y - coordinate

Substitute \( x = 2 \) into the function \( g(x)=-x^{2}+4x - 3 \). So \( g(2)=-(2)^{2}+4\times(2)-3=-4 + 8-3=1 \).

Answer:

The vertex of the parabola \( g(x)=-x^{2}+4x - 3 \) is \( (2,1) \)