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Ramiro drew the graph below.

On a coordinate plane, a parabola opens up and has a vertex at (4, 0). It goes through (2, 4) and (6, 4).

Which equation represents the data in the graph?
y = x squared minus 8 x + 16
y = 5.5 x squared minus 0.5 x + 4
y = x squared + 4 x + 4
y = 2.5 x squared minus 0.5 x + 4

Respuesta :

lonieburger
The equation x squared minus 8x+16 represents the data in the graph because if you use the -b/2a x=4. Then if you plug in the 4 for the x in the equation you would come out with the vertex of (4,0). Hope this helps.

[tex]y=x^{2} -8x+16[/tex] equation represents the data in the parabola.

What is parabola?

"A parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped."

We have

Direction of parabola: opens up

Vertex of parabola: (4,0)

Parabola goes through (2,4) and (6,4)

We have

[tex]y=ax^{2} +bx+c[/tex]......................(1)

Substitute (x, y) = (4, 0) in equation (1)

[tex]0= a.4^{2}+b.4+c[/tex]

⇒ [tex]0=16a+4b+c[/tex]

⇒[tex]16a+4b+c =0[/tex].....................(2)

Substitute (x, y) = (2, 4) in equation (1)

[tex]4= a.2^{2}+b.2+c[/tex]

⇒[tex]4a+2b+c =4[/tex]......................(3)

Substitute (x, y) = (6, 4) in equation (1)

[tex]4= a.6^{2}+b.6+c[/tex]

⇒[tex]36a+6b+c =4[/tex].....................(4)

By solving equations (2), (3) and (4)

a = 1

b = -8

c = 16

Substitute a, b and c values in equation (1)

⇒ [tex]y=x^{2} -8x+16[/tex]

Hence, [tex]y=x^{2} -8x+16[/tex] equation represents the data in the parabola.

Learn more about parabola here

https://brainly.in/question/15044480

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