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How do I find the answer to this question?

How do I find the answer to this question?-example-1
User Mockash
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4 votes

Answer:

d.

Explanation:

various possibilities.

first suggestion : remember the general form of a parabola :

y = (x - h)² + k

with (h, k) being the the vertex (the maximum or minim point of the parabola).

as we can see, the vertex is (3, -1).

so, the correct equation is

y = (x - 3)² - 1

second suggestion : we have 4 points :

2 zeroes (2, 0) and (4, 0)

the y-intercept (0, 8)

and the vertex again (3, -1)

in general, the equating equation can be built by factorization around the zeros :

y = a×(x - zero1)(x - zero2)

in our case that is

y = a×(x - 2)(x - 4)

let's do the multiplication :

y = a×(x² - 2x - 4x + 8) = (x² - 6x + 8)

"a" we get by using the 3rd point like the y-intercept :

8 = a×(0² - 6×0 + 8) = 8a

a = 1

a > 0 confirms what we are seeing : the parabola opens upwards.

to bring

y = x² - 6x + 8

into the standard form

y = (x - h)² + k

we need to complete the square in the expression :

(x - h)² = x² - 2hx + h²

now compare this to our real expression

x² - 2hx + h² = x² - 6x + 8

x² = x² check

-2hx = -6x

-2h = -6

-h = -3

h = 3

h² = 9

8 = 9 - 1 = h² - 1

so,

y = x² - 6x + 8 = (x - 6x + 9) - 1 = (x - 3)² - 1

User Can Karabag
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