Question

What is the vertex of the graph of y = 2(x – 3)2 + 4?

(4, 3)

(4, –3)

(3, 4)

(–3, 4)

Answer 1

Is there a picture of the graph?

Answer 2

\(ax^2+bx+c\) has vertex at \(\frac{-b}{2a}\)

Answer 3

and the point is given by
\((\frac{-b}{2a},f(\frac{-b}{2a}))\)

Answer 4

\(2(x-3)^2+4=2(x^2-6x+9)+4=2x^2-12x+18+4 = 2x^2-12x+22\)
so the vertex is at \(x=\frac{12}{4}=3\)
plug that into the polynomial and get
f(3) = 4
so the vertex is at (3,4)

Answer 5

*so the vertex is (3,4)

Answer 6

thanks