Find the X intercepts of each quadratic relation without graphing: y=x^2-2x-15 , y=x^2+11x+24 , y=-x^2-3x+18 , y=-x^2-x+30

Answer 1

To find the x-intercepts of a quadratic relation, we need to set y equal to zero and solve for x.

1. For y = x^2 - 2x - 15:
x^2 - 2x - 15 = 0

Factor the quadratic:
(x - 5)(x + 3) = 0

Set each factor to zero:
x - 5 = 0 or x + 3 = 0
x = 5 or x = -3

The x-intercepts are x = 5 and x = -3.

2. For y = x^2 + 11x + 24:
x^2 + 11x + 24 = 0

Factor the quadratic:
(x + 3)(x + 8) = 0

Set each factor to zero:
x + 3 = 0 or x + 8 = 0
x = -3 or x = -8

The x-intercepts are x = -3 and x = -8.

3. For y = -x^2 - 3x + 18:
-x^2 - 3x + 18 = 0

Rearrange the quadratic:
x^2 + 3x - 18 = 0

Factor the quadratic:
(x + 6)(x - 3) = 0

Set each factor to zero:
x + 6 = 0 or x - 3 = 0
x = -6 or x = 3

The x-intercepts are x = -6 and x = 3.

4. For y = -x^2 - x + 30:
-x^2 - x + 30 = 0

Rearrange the quadratic:
x^2 + x - 30 = 0

Factor the quadratic:
(x + 6)(x - 5) = 0

Set each factor to zero:
x + 6 = 0 or x - 5 = 0
x = -6 or x = 5

The x-intercepts are x = -6 and x = 5.