Question

Find the equation, f(x) = a(x-h)2 + k, for a parabola that passes through the point (1,-7) and has (2,- 4) as its vertex. What is the standard form of the equation?
a.The vertex form of the equation is f(x) = -3(x + 2)2 - 4. The standard form of the equation is f(x) = 3x2 + 12x − 8.
b.The vertex form of the equation is f(x) = 3(x + 2)2 + 4. The standard form of the equation is f(x) = 3x2 − 12x −16.
c.The vertex form of the equation is f(x) = −3(x - 2)2 −4. The standard form of the equation is f(x) = −3x2 + 12x − 16.
d.The vertex form of the equation is f(x) = 3(x + 2)2− 4. The standard form of the equation is f(x) = 3x2 − 12x + 8.

Answer 1

$(h;\ k)\ -\ \text{the coordinates of the vertex}$

$\text{therefore we have}\ f(x)=a(x-2)^2-4$
 
$\text{a parabola that passes through the point (1,-7)}$

$\text{substitute the coordinates of the point (1;-7) to the equation:}$

$(1;-7)\to x=1;\ y=-7\\\\-7=a(1-2)^2-4\\\\-7=a(-1)^2-4\\\\-7=a-4\ \ \ |+4\\\\a=-3$


$Answer:\ \text{c.The vertex form of the equation is}\ f(x)=-3(x-2)^2-4.\\\text{The standard form of the equation is}\ f(x)=-3x^2+12x-16$