Algebra

y = (x + 2)^2 - 4

Step-by-step solution with explanation

Final Answer

and

Step-by-step solution

1

Understand what we are solving

We need to find the x-intercepts (solutions), which means we set y = 0 and solve for x.
2

Set y equal to zero

Setting y = 0 finds where the parabola crosses the x-axis. These crossing points are the solutions.
3

Move 4 to the left side

Add 4 to both sides to isolate the squared term. This makes it easy to take the square root next.
4

Take the square root of both sides

When you take the square root to solve an equation, you must include both the positive and negative roots. That gives us .
5

Solve for x using the positive root

Subtract 2 from both sides of the positive case to get the first solution.
6

Solve for x using the negative root

Subtract 2 from both sides of the negative case to get the second solution.
7

State both solutions

A quadratic equation can have up to two solutions. Both values make the original equation true when y = 0.

Understanding this problem

Learning Insight

This equation is already in vertex form , where the vertex is at . Because the vertex is below the x-axis and the parabola opens upward, it must cross the x-axis at exactly two points — which matches our two solutions.

Quick Tip

In vertex form , you can jump straight to setting , then . Skip rearranging step by step and mentally 'peel off' one layer at a time.

Common Mistake

Students often forget the when taking the square root and only find one solution (usually ), completely missing the second solution .