Question

1. three quadratic functions are represented below. which function has the highest maximum value?

a
$f(x) = -(x - 1)^2 + 6$
b
graph of a parabola
c

x	y
0	0
1	3
2	4
3	3
4	0

Explanation:

Step1: Analyze Function A

The function is in vertex form \( f(x) = -(x - 1)^2 + 6 \). For a quadratic function in the form \( f(x)=a(x - h)^2 + k \), the vertex is \((h,k)\). Since \( a=-1<0 \), the parabola opens downward, so the vertex \((1,6)\) is the maximum point. Thus, the maximum value of A is \( 6 \).

Step2: Analyze Function B

From the graph, we can estimate the vertex. The parabola opens downward (since it has a maximum). By looking at the grid, we can see that the vertex (peak) seems to be at a y - value less than 6. Let's assume we can visually check: the graph's peak is lower than 6 (for example, if we count the grid squares, the y - coordinate of the vertex is likely 4 or 5, but definitely less than 6).

Step3: Analyze Function C

We have a table of values. The function is symmetric (since \( f(0)=f(4) = 0 \), \( f(1)=f(3)=3 \)), so the vertex is at \( x = 2 \). When \( x = 2 \), \( y = 4 \). So the maximum value of C is \( 4 \).

Answer:

Function A (with \( f(x)=-(x - 1)^2+6 \)) has the highest maximum value.