Question

For the quadratic equation y=x ² −2x−8, what are the x-intercepts?

A) x=−2 and x=4
B) x=−4 and x=2
B) x=−4 and x=2
D) x=3 and x=−5

Answer 1

`\Large \textsf{Read below}`

Step-by-step explanation:

`\Large \text{$ \sf y = x^2 - 2x - 8$}`

`\Large \text{$ \sf a = 1$}`

`\Large \text{$ \sf b = -2$}`

`\Large \text{$ \sf c = -8$}`

`\Large \text{$ \sf \Delta = b^2 - 4.a.c$}`

`\Large \text{$ \sf \Delta = (-2)^2 - 4.1.(-8)$}`

`\Large \text{$ \sf \Delta = 4 + 32$}`

`\Large \text{$ \sf \Delta = 36$}`

`\Large \text{$ \sf x = (-b \pm √(\Delta))/(2a) = (2 \pm √(36))/(2) \rightarrow \begin{cases}\sf{x' = (2 + 6)/(2) = 4}\\\\\sf{x'' = (2 - 6)/(2) = -2}\end{cases}$}`

`\Large \boxed{\boxed{\text{$ \sf S = \{-2,\:4\}$}}}`

Answer 2

The x-intercepts of the quadratic equation y=x²−2x−8 are x = -2 and x = 4.

Step-by-step explanation:

The quadratic equation y=x²−2x−8 can be rearranged into the form ax²+bx+c=0, where a=1, b=-2, and c=-8. To find the x-intercepts, we need to solve the equation when y=0. Substituting y=0 into the equation, we get:

0=x²−2x−8

Using the quadratic formula, x = (-b ± √(b²-4ac))/(2a), we can calculate the x-intercepts:

x = (-(-2) ± √((-2)²-4(1)(-8)))/(2(1))

x = (2 ± √(4+32))/2

x = (2 ± √(36))/2

x = (2 ± 6)/2

Therefore, the x-intercepts are x = -2 and x = 4.