Question

ALGEBRA!!

find the equation (f(x)=a(x-h)^2+k) for a parabola containing point (2,-1) and having (4,-3) as a vertex. what is the standard form of the equation
A.)the vertex form is f(x)=x^2-3. The standard form is f(x)=1/2x^2-4x+6
B.)the vertex form is f(x)=1/2(x-3)^2+4 . The standard form is f(x)=x^2-4x+5
C.)the vertex form is f(x)=1/2x^2-4x+3. The standard form is f(x)=1/2x^2-4x-8
D.)the vertex form is f(x)=1/2(x-4)^2-3. The standard form is f(x)=1/2x^2-4x+5
PLEASE HELP

Answer 1

Vertex form: y = a(x-h)^2 + k

Let's find a.

Substitute vertex and point on parabola into vertex equation:

-1 = a(2-4)^2 - 3

Solve for a:

-1 = a*4 - 3

2 = a*4

a = 1/2

The vertex equation for this parabola is y = 1/2(x-4)^2 - 3

By elimination, the answer is D, y = 1/2(x-4)^2 and y = (1/2)x^2 - 4x + 5