Question

What are the x-intercepts of the quadratic equation?: y = (2x - 3) (x - 6)

Answer 1

To find the x-intercepts of the quadratic equation \( y = (2x - 3)(x - 6) \), we need to set \( y \) to 0 and solve for \( x \):

\[
0 = (2x - 3)(x - 6)
\]

To find the x-intercepts, we set each factor equal to zero:

1. Set \( 2x - 3 = 0 \):
\[
2x = 3 \\
x = \frac{3}{2}
\]

2. Set \( x - 6 = 0 \):
\[
x = 6
\]

Thus, the x-intercepts of the quadratic equation are:

\[
x = \frac{3}{2} \quad \text{and} \quad x = 6
\]

In coordinate form, the x-intercepts are \( \left(\frac{3}{2}, 0\right) \) and \( (6, 0) \).