In the diagram, point D divides line segment AB in the ratio of 5:3. If line segment AC is vertical and line segment CD is horiz
ontal, what are the
coordinates of point C?
B = (102)
C = (?)
D
A = (2-6)
OA (5,-3)
OB. 17.-1)
OC (2.-1)
OD. (2-3)
coordinates of point C?
B = (102)
C = (?)
D
A = (2-6)
OA (5,-3)
OB. 17.-1)
OC (2.-1)
OD. (2-3)
1 answer:
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Answer:
One possible equation is , which is equivalent to
.
Step-by-step explanation:
The factor theorem states that if (where
is a constant) is a root of a function,
would be a factor of that function.
The question states that and
are
-intercepts of this function. In other words,
and
would both set the value of this quadratic function to
. Thus,
and
would be two roots of this function.
By the factor theorem, and
would be two factors of this function.
Because the function in this question is quadratic, and
would be the only two factors of this function. In other words, for some constant
(
):
.
Simplify to obtain:
.
Expand this expression to obtain:
.
(Quadratic functions are polynomials of degree two. If this function has any factor other than and
, expanding the expression would give a polynomial of degree at least three- not quadratic.)
Every non-zero value of corresponds to a distinct quadratic function with
-intercepts
and
. For example, with
:
, or equivalently,
.
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