Question

The graph of a function in the form f(x) a(x - h)2 +k is shown. Use the graph to find an equation for f(x).

Answer 1

O.K.

(h; k) are the coordinates of the vertex.

On the graph are (3; 4), therefore we have:


`f(x)=a(x-3)^2+4`

We have the x-intercept (1; 0) → x = 1; y = 0.
Substitute them in the equation:


`0=a(1-3)^2+4\\\\0=a(-2)^2+4\\\\4a+4=0\ \ \ |-4\\\\4a=-4\ \ \ \ |:4\\\\a=-1`

so. We have the answer:


`\boxed{f(x)=-(x-3)^2+4}`