Solve y = -27 + 3x²: Finding X-Axis Intersection Points

To solve for the intersection points of the function $y=-27+3x^2$ with the x-axis, follow these steps:

• Step 1: Set the function equal to zero because intersections with the x-axis occur when $y = 0$.
  So we solve $-27 + 3x^2 = 0$.
• Step 2: Simplify and solve the equation.
  Start with $3x^2 = 27$.
• Step 3: Divide both sides by 3 to isolate $x^2$.
  $x^2 = 9$.
• Step 4: Solve for $x$ by taking the square root of both sides.
  Thus, $x = \pm \sqrt{9}$, so $x = 3$ or $x = -3$.

Therefore, the points of intersection are $(3, 0)$ and $(-3, 0)$.

The correct choices from the answer list are 1: $(3,0)$ and 2: $(-3,0)$. Therefore, answer choice 4: Answers $a$ and $b$ are correct is correct.