Respuesta :

siamese512

Answer:

look below

Step-by-step explanation:

The vertex  will be found at (4,2)   and we can write that :



(y - 2) = (a)(x - 4)^2       and since (8,6)   is on the curve, we can solve for a



(6 -2)  = (a) (8 - 4)^2    simplify



4 = (a)(4)^2



4 = (a)16   →    a = 4/16  = 1/4



Since the x coordinate of the vertex is given by -b/ (2a)  we have that   -b/[2 (1/4)]  = 4   → -b / (1/2) = 4 → -b = 2 → b = -2



And using the fact that  (4,2)  is on the graph, we can find c, thusly :



y = ax^2 + bx + c  ......so......



2 = (1/4)(4)^2 -2(4) + c



2 = 4 - 8 + c



2  = -4 + c



c = 6



Then a*b*c =  (1/4) (-2) (6)    =  (1/4)(-12)    = -3

The vertex at (4,2)  can be found by

(y - 2) = (a)(x - 4)^2

∵ (8,6)  is lying on the curve

So, (6 -2)  = (a) (8 - 4)^2  

by simplify, we get

4 = (a)(4)^2

4 = (a)16

a = 4/16 = 1/4

Since the coordinate of x-axies of the vertex is given by -b/(2a)  we have

b/[2 (1/4)]  = 4

-b / (1/2) = 4

-b = 2

b = -2

by using the point that  (4,2)  is on the graph, we can find c

y = ax^2 + bx + c

2 = (1/4)(4)^2 -2(4) + c

2 = 4 - 8 + c

2  = -4 + c

c = 6

∴ a*b*c

=  (1/4) (-2) (6)

=  (1/4)(-12)

= -3

Why do we graph equations?

Diagrams of direct conditions are particularly successful for addressing connections between things that change at a steady rate, and they frequently improve than words or numerical conditions alone.

How to depict the chart of a quadratic capability?

The diagram of a quadratic capability is known as a parabola and has a bent shape. One of the primary concerns of a parabola is its vertex. It is the most noteworthy or the absolute bottom on the diagram.

Learn more about Graph here

brainly.com/question/14323743

#SPJ2

Otras preguntas