What is the vertex of f(x)2x2 plus 16x plus 9?

Answer 1

To find the vertex of the quadratic function ( f(x) = 2x^2 + 16x + 9 ), we can use the vertex formula. The x-coordinate of the vertex is given by ( x = -\frac{b}{2a} ), where ( a = 2 ) and ( b = 16 ). Thus, ( x = -\frac{16}{2 \cdot 2} = -4 ). Substituting ( x = -4 ) back into the function gives ( f(-4) = 2(-4)^2 + 16(-4) + 9 = 2(16) - 64 + 9 = -64 + 9 + 32 = -23 ). Therefore, the vertex is at the point ( (-4, -23) ).