Solve y = x² - 49: Finding X-Intercepts of a Quadratic Function

To determine the points of intersection of the function $y = x^2 - 49$ with the x-axis, we set $y = 0$. This gives us the equation:

$x^2 - 49 = 0$

We can solve this equation by factoring or using the square root method:

• Recognize $x^2 - 49$ as a difference of squares since $49 = 7^2$.
• The equation can be rewritten and factored as: $(x - 7)(x + 7) = 0$.

Setting each factor equal to zero gives:

$x - 7 = 0$ or $x + 7 = 0$

This simplifies to:

$x = 7$ or $x = -7$

Thus, the points of intersection are where the function crosses the x-axis, at the coordinates $(7, 0)$ and $(-7, 0)$.

Referring to the given answer choices, the correct choice is:

$(7, 0), (-7, 0)$

Therefore, the points of intersection of the function $y = x^2 - 49$ with the x-axis are $(7, 0)$ and $(-7, 0)$.