Question

$y=x^2-6x+8$
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. $y=(x-2)(x-4)$

Answer 1

The correct option is D $y=(x-2)(x-4)$

Given, $y=x^2-6x+8$

For knowing the $x$ intercepts of the parabola, $y$ needs to be equated to $0$.

Doing that, we get $0=x^2-6x+8$

$\Rightarrow x^2-4x-2x+8=0$

$\Rightarrow x(x-4)-2(x-4)=0$

$\Rightarrow (x-2)(x-4)=0$

Thus, the original equation can be written as $y=(x-2)(x-4)$