Question

Write the equation of the parabola in vertex form. vertex (3,3), point (1,-5)
f(x)=

Answer 1

The equation of the parabola in vertex form is f(x) = -2(x-3)^2 + 3.

Step-by-step explanation:

The equation of a parabola in vertex form is given by f(x) = a(x-h)2 + k, where (h, k) represents the vertex.

In this case, the given vertex is (3,3). Substituting the values into the equation, we get f(x) = a(x-3)2 + 3.

To find the value of 'a', we can substitute the coordinates of the other point (1,-5) into the equation and solve for 'a'. Substituting (1,-5), we get -5 = a(1-3)2 + 3. Simplifying the equation, we have -5 = 4a + 3.

Solving for 'a', we get a = -2.

Therefore, the equation of the parabola in vertex form is f(x) = -2(x-3)2 + 3.