Question

Write the function that describes a parabola that has a vertex at (3,-4) and goes through the point (5,-12).

Answer 1

Answer: The answer is f(x) = - 2x²+12x-22.

Step-by-step explanation:  We are given to write the function describing a parabola with vertex (3, -4)  and passing through the point (5, -12).

We know that the standard form of a parabola with vertex (h, k) is given by

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

Here (h, k) = (3, -4), so we have

$f(x)-(-4)=a(x-3)^2\\\\\Rightarrow f(x)+4=a(x-3)^2.~~~~~~~~~~~(I)$

Also, the parabola is passing through the point (5, -12), so

$-12+4=a(5-3)^2\\\\\Rightarrow -8=a\times 4\\\\\Rightarrow a=-2.$

Substituting the value of 'a' above in equation (I), we have

$f(x)+4=-2(x-3)^2\\\\\Rightarrow f(x)=-2(x^2-6x+9)-4\\\\\Rightarrow f(x)=-2x^2+12x-22.$

Thus, the answer is f(x) = - 2x²+12x-22..