Question

The quadratic equation $y=x^2-8x-48$ can also be represented as

• A. $y=(x-8{)}^2-16$
• B. $y=(x-8{)}^2+16$
• C. $y=(x-8)(x+6)$
• D. $y=(x-12)(x+4)$

Answer 1

The correct option is D $y=(x-12)(x+4)$

Step 1: Keep all terms containing x on one side. Move the constant to the right.

$x^2-8x-48=0$

Step 2: Take half of the x-term coefficient and square it. Add this value to both sides.

The half of the x-term coefficient = -4

After squaring we have $(-4{)}^2=16.$

When we add 16 to both sides we have: $x^2-8x+16=48+16$

Write the perfect square on the left.

$(x-4{)}^2=64$

Take the square root of both sides.

$X–4=\pm \sqrt{64}$

$x=4\pm 8$

Therefore, x = -4, 12