Question

question 9
cc.2.2.hs.d.10
find the vertex for
y = x² - 8x - 4
○ (4, -20)
○ (4, 29)
○ (8, -4)
○ (4, 44)

Explanation:

Step1: Recall vertex formula for parabola

For a quadratic function \( y = ax^2 + bx + c \), the x - coordinate of the vertex is given by \( x =-\frac{b}{2a} \). In the function \( y=x^{2}-8x - 4 \), we have \( a = 1 \), \( b=-8 \), and \( c=-4 \).

Step2: Calculate x - coordinate of vertex

Substitute \( a = 1 \) and \( b=-8 \) into the formula \( x=-\frac{b}{2a} \). We get \( x =-\frac{-8}{2\times1}=\frac{8}{2}=4 \).

Step3: Calculate y - coordinate of vertex

Substitute \( x = 4 \) into the function \( y=x^{2}-8x - 4 \). Then \( y=(4)^{2}-8\times4 - 4=16-32 - 4=16-(32 + 4)=16 - 36=-20 \).

Answer:

\( (4, - 20) \) (corresponding to the option: (4, -20))