Question

Write the equation of the parabola in vertex form. vertex (3,1), point (2, - 6) f(x) =?

Answer 1

Answer:

$f(x)=-7(x-3)^2+1$

Step-by-step explanation:

Vertex form of a quadratic is given by:

$f(x)=a(x-h)^2+k$

Where (h, k) is the vertex and a is the leading coefficient.

We are given that the vertex is (3, 1). Hence, h = 3 and k = 1. By substitution:

$f(x)=a(x-3)^2+1$

We are also given a point (2, -6). This means that when x = 2, f(x) = -6. Hence:

$-6=a((2)-3)^2+1$

Solve for a. Subtract:

$-6=a(-1)^2+1$

Simplify:

$-6=a+1$

Therefore:

$a=-7$

Hence, our quadratic is:

$f(x) = -7 (x-3)^2 + 1$