Help with quadratic function?

Have you really studied quadratic curves first? Do you know that y = ax^2 +bx + c has x = -b/2a as the axis?

The axis is x = 3 so b = -6. and y= x^2 -6x + c passes through (5, 2) means 2 = a(25) - 6(5) + c means c = 7. Where is the difficulty?

Because it is symmetric about the line x=3

Point (1,2) is also on the curve

2 = 25+5b+c so -23 = 5b+c

2 = 1+b+c so 5 = 5b+5c Subtract equations

28 = 4c

c = 7

the answer is 4.

since the graph is symmetric about the line x=3.

the graph passes through the points (5,2) and (1,2). We have two equations 2=25+5b+c,2=1+b+c and solving for c we get c=4

hope it was helpful.

Express x^2+bx+c in the completed square form so that x^2+bx+c=(x+p)^2+q and since graph

is symmetrical about line x=3, p=-3 so x^2+bx+c=(x-3)^2+q=y

You know that when x=5, y=2 so 4+q=2 giving q=-2 this then gives y=x^2-6x-7 so c=-7