### Home > INT2 > Chapter 5 > Lesson 5.2.1 > Problem5-65

5-65.

Determine the exact $x$‑intercepts of $y = (x + 4)^2 − 7$.

Let $y = 0$, then solve for $x$.

$\text{The}\:x\text{-intercepts are}\: (-4+\sqrt{7},0)\; \text{and}\; (-4-\sqrt{7},0).$

1. What are the approximate $x$-intercepts? Sketch a graph of the parabola.

2. Refer to the Math Notes box in this lesson. Are the solutions to the equation $0 = (x + 4)^2 - 7$ rational or irrational numbers? Explain.

Is $7$ a perfect square?

3. What are the coordinates of the vertex of the parabola? Is your answer exact or approximate?

$(−4, −7)$