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y=x^(2)-6x+8 The equation above repres...

`y=x^(2)-6x+8`
The equation above represents a parabola in the xy-plane. Which of the following equivalent forms of the equation displays the x-intercepts of the parabola as constants or coefficients?

A

`y-8=x^(2)-6x`

B

`y+1=(x-3)^(2)`

C

`y=x(x-6)+8`

D

`y=(x-2)(x-4)`

Text Solution

Verified by Experts

Choice D is correct. The x-intercepts of the parabola represented by `y = x^(2) − 6x + 8` in the xy-plane are the values of x for which y is equal to 0. The factored form of the equation, y = (x − 2)(x − 4), shows that y equals 0 if and only if x = 2 or x = 4. Thus, the factored form, y = (x − 2)(x − 4), displays the x-intercepts of the parabola as the constants 2 and 4.
Choices A, B, and C are incorrect because none of these forms shows the x-intercepts 2 and 4 as constants or coefficients.
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