Question

If y=x^2+8x+9, what’s the 2 x-intercepts of the parabola?

Answer 1

x = -4 ±√(7)

or in decimal:

x = -1.35 or -6.65

Explanation:

y=x²+8x+9

note x-intercepts occur when y = 0,

Hence, x²+8x+9 = 0 (solve this using your favorite method. We will complete the square)

x²+8x+9 = 0 (rearrange)

x²+8x = -9 (complete the square and add factor to both sides)

x² + 8x + (8/2)² = -9 + (8/2)²

[ x + (8/2) ]² = -9 + (8/2)²

[ x + 4 ]² = -9 + (4)²

[ x + 4 ]² = -9 + 16

[ x + 4 ]² = 7

x+4 = ±√(7)

x = -4 ±√(7)

x = -1.35 or -6.65