Solving Square Roots

A square root of a number x is a value y such that y² = x. For example, the square root of 9 is 3, since 3² = 9.

To solve an equation using square roots, isolate the variable term on one side of the equation and then take the square root of both sides. Remember to consider both the positive and negative roots.

It means that the graph of the equation does not intersect the x-axis, indicating that the solutions are imaginary.

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the solutions of the quadratic equation ax² + bx + c = 0.

The discriminant is the part of the quadratic formula under the square root, b² - 4ac. It determines the nature of the roots: if positive, there are two real solutions; if zero, one real solution; if negative, two imaginary solutions.

b = 3, b = -3.

x = ±1.

By observing the points where the graph intersects the x-axis. Each intersection represents a real solution.

It means the graph of the equation touches or crosses the x-axis at two distinct points.

The vertex is the highest or lowest point of the parabola, representing the maximum or minimum value of the function.