Question

What is the equation for this?

Answer 1

f(x) = -(x - 2)^2 + 1

or in standard form it is

f(x) = -x^2 + 4x - 3.

Explanation:

The graph opens downwards so the leading coefficient is negative. The vertex is at x = 2 and y = 1 so we can write the equation in vertex form as:

f(x) = a(x - 2) + 1 where a is some constant.

Now the zeroes of the function are (1, 0 ) and (3, 0).

So we can plug in one of these ( say (1,0) ) into the equation to find the value of a:

0 = a(1 - 2) + 1

0 = a - 2a + 1

0 = -a + 1

a = 1

So our equation is -1(x - 2)^2 + 1

= -( x - 2)^2 + 1