Subjects algebra

Parabola X Intercepts 362Dfc

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1. The problem states: The parabola $y = 3(x - 4)(x + 2)$ has $x$-intercepts at $(-4, 0)$ and $(2, 0)$. We need to verify if this is true or false. 2. Recall that $x$-intercepts occur where $y=0$. To find the $x$-intercepts, set the equation equal to zero: $$0 = 3(x - 4)(x + 2)$$ 3. Since $3 \neq 0$, the product is zero only if one of the factors is zero: $$x - 4 = 0 \quad \text{or} \quad x + 2 = 0$$ 4. Solving these gives: $$x = 4 \quad \text{or} \quad x = -2$$ 5. Therefore, the $x$-intercepts are at points $(4, 0)$ and $(-2, 0)$. 6. The problem claims the intercepts are at $(-4, 0)$ and $(2, 0)$, which is incorrect. 7. Hence, the statement is **False**.