Question

given $y = x^2 + 10x + 8$, determine the turning point.

a. $(-5,17)$
b. none of the above
c. $(5, 17)$
d. $(-5,-17)$
e. $(5, -17)$

Explanation:

Step1: Recall vertex formula for parabola

For a quadratic function \( y = ax^2 + bx + c \), the x - coordinate of the vertex (turning point) is given by \( x=-\frac{b}{2a} \). Here, \( a = 1 \), \( b = 10 \), so \( x=-\frac{10}{2\times1}=- 5 \).

Step2: Find y - coordinate

Substitute \( x=-5 \) into the function \( y=x^{2}+10x + 8 \). Then \( y=(-5)^{2}+10\times(-5)+8=25-50 + 8=-17 \).

Answer:

d. (-5,-17)