Wirte the following equations in vertex form: a(x-h)^2 + K?

Question

y = -1/5x^2 + 4/5x + 11/5

Answer 1

the first thing you need to do is to factor out -1/5
that will give
y= -1/5 ( x^2 -4x - 11)
the next thing that you need to do is complete the square for the quadratic
y = -1/5 [( x^2 - 4x + ___ ) - 11 - ___ ] the blanks would be the number that would make a trinomial square. The blank would be half of 4 squared. ( which is 4 ) so this gives us
y = - 1/5 [ ( x^2 - 4x + 4 ) - 11 - 4 ]
simplifying would give
y = - 1/5 [ ( x^2 - 4x + 4) - 15 ]
rewrite the trinomial as a binomial square and distribute the -1/5 to both terms and you will have
y = -1/5 ( x - 2 )^2 +3
where the vertex would be ( 2, 3 )

I hope you could follow all of that.

Answer 2

y = (-1/5)x^2 + (4/5)x + (11/5)
y = ((-1/5)x^2 + (4/5)x) + (11/5)
y = (-1/5)(x^2 - 4x) + (11/5)
y = (-1/5)(x^2 - 4x + 4 - 4) + (11/5)
y = (-1/5)((x^2 - 4x + 4) - 4) + (11/5)
y = (-1/5)((x - 2)^2 - 4) + (11/5)
y = (-1/5)(x - 2)^2 + (4/5) + (11/5)
y = (-1/5)(x - 2)^2 + (15/5)
y = (-1/5)(x - 2)^2 + 3

so

a = (-1/5)
h = -2
K = 3

Answer 3

you're able to plug interior the vertex first into your equation. y=a(x-a million)^2-19 you put in x-a million via fact once you positioned x-a million=0 you get x=a million. -19 maintains to be a similar via fact its already on the different facet of y. it would be y+19=a(x-a million)^2 in case you had finished vertex style, returned, so as that in case you positioned y+19=0 you may get y=-19. next you're able to plug interior the 2d pair of things. 0=a(-18-a million)^2-19 you're able to unravel for a now. 0+19 =19, and on the excellent suited facet -18-a million is -19, and that squared is 361. now you have 19=361a so a=19/361 your very final formulation is y=19/361(x-a million)^2-19

Answer 4

X=2 Y=3 is the vertex. Compliments of the programs offered at TICALC.org check it out. Its awesome. Download programs from internet to calculator perfect.

Answer 5

-5y = x^2 -4x -11= (x-2)^2 -15 So
y = -1/5(x-2)^2 +3