b The function increases until it reaches the vertex.
C
c y=1
Practice makes perfect
a Notice that the function is written in graphing form, also called vertex form, which means we can identify its vertex directly. For this purpose we have to make the right-hand side of our function match the right-hand side of the graphing form.
Graphing Form:& y=a(x- h)^2+ k
Vertex:& ( h, k)
To identify the vertex we have to rewrite the right-hand side to match the graphing form.
Graphing Form:& y=- (x-( - 4))^2+ 1
Vertex:& ( - 4, 1)
As we can see, the parabola has its vertex at (- 4,1). Additionally, notice that the coefficient to (x+4)^2 is negative, which means the parabola opens downwards.
b Looking at the graph from Part A, see that the function increases until it reaches the maximum value, which is found at the vertex. The x-coordinate of the vertex equals - 4, so the function is increasing for x such that x ≤ -4.
c The maximum value refers to the greatest y-value that a function can give, and it is found at the vertex. Examining the diagram, we see that the maximum value is y=1.
