Determine the Intersection Points of y=(-2x+4)(x+3) with the X-Axis

To solve the problem, we need to find the x-intercepts of the quadratic function:

$y = (-2x + 4)(x + 3)$

The x-intercepts occur where the function equals zero, i.e., when $y = 0$. Since the function is in factored form, we apply the zero-product property:

• Set each factor equal to zero:
• $(-2x + 4) = 0$
• $x + 3 = 0$

Next, solve each equation for $x$:

• For $(-2x + 4) = 0$:
• Subtract 4 from both sides: $-2x = -4$
• Divide by -2: $x = 2$
• For $x + 3 = 0$:
• Subtract 3 from both sides: $x = -3$

Therefore, the function intersects the x-axis at the points $(-3, 0)$ and $(2, 0)$.

Additionally, when correlating with answer choices, choice 2 matches our derived solution:

$(-3, 0), (2, 0)$