Question

om 5.1, 5.2, 5.3
score: 7/14 answered: 3/7
question 4
graph the following:
$f(x) = 2x^2 + 12x + 17$
the vertex is

Explanation:

Step1: Find x-coordinate of vertex

For a quadratic \( f(x)=ax^2 + bx + c \), vertex x - coord is \( x = -\frac{b}{2a} \). Here, \( a = 2 \), \( b = 12 \). So \( x = -\frac{12}{2\times2}=-\frac{12}{4}=-3 \).

Step2: Find y-coordinate of vertex

Substitute \( x = -3 \) into \( f(x) \): \( f(-3)=2(-3)^2 + 12(-3)+17 \). Calculate: \( 2\times9 - 36 + 17 = 18 - 36 + 17 = -1 \).

Answer:

\((-3, -1)\)