Question

Without graphing, determine the number of x-intercepts that each relation has.
y = (2x - 3)(x + 9)

Answer 1

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

Setting y equal to zero in the given relation, we get:
0 = (2x - 3)(x + 9)

To find the x-intercepts, we need to solve for x in the above equation. Since the product of two factors is zero, this means that at least one of the factors must be zero.

Setting each factor equal to zero, we get:
2x - 3 = 0 or x + 9 = 0

Solving these equations for x, we get:
2x = 3 or x = -9

Dividing both sides of the first equation by 2, we get:
x = 3/2

Therefore, the relation y = (2x - 3)(x + 9) has two x-intercepts: x = 3/2 and x = -9.