Find the vertex and the maximum or minimum value

Question

f(x)=3(x-7)^2+3

Answer 1

The equation you've given here is in one of the standard forms of a parabola. The generic version is:

f(x) = a(x-h)² + k

a is the amplitude of the graph, which determines direction and how much the graph is stretched or squashed.

the values of h and k tell you the vertex point (h, k)

 

In your equation, you have a = 3. Since this is positive, it means the parabola opens upward, like a U. The y-value of the vertex is the minimum value of the graph.

 

Also from your equation, h = 7 and k = 3. Your vertex is the point (7, 3) and 3 is the minimum value.

 

Be careful with the value of h, since the formula has subtraction in it. A value (x-7) means h = +7, while (x+7) would mean that h = -7.