Question

question 4 of 10
find the vertex of the function given below.
y = 2x² + 4x + 1
a. (-1, -1)
b. (3, -4)
c. (-4, 9)
d. (1, 7)

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 \( y = 2x^2+4x + 1 \), \( a = 2 \), \( b = 4 \), \( c = 1 \).
So, \( x=-\frac{4}{2\times2}=-\frac{4}{4}=- 1 \).

Step2: Find the y - coordinate of the vertex

Substitute \( x=-1 \) into the function \( y = 2x^2+4x + 1 \).
\( y=2\times(-1)^2+4\times(-1)+1 \)
\( y = 2\times1-4 + 1 \)
\( y=2-4 + 1=-1 \)

Answer:

A. (-1, -1)