Question

what are the x-intercepts of the quadratic equation below?
y=(2x — 3) (x—6)

Answer 1

To find the x-intercepts of the quadratic equation given in the factored form \( y = (2x - 3)(x - 6) \), we need to set \( y \) equal to zero and solve for \( x \).

Setting the equation to zero:

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

Now, we can set each factor equal to zero:

1. \( 2x - 3 = 0 \)
2. \( x - 6 = 0 \)

Solving the first equation:

\[
2x - 3 = 0 \implies 2x = 3 \implies x = \frac{3}{2}
\]

Solving the second equation:

\[
x - 6 = 0 \implies x = 6
\]

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

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

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