Solving Square Roots

Front

What is a square root?

Back

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.

Front

How do you solve an equation using square roots?

Back

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.

Front

What does it mean if a quadratic equation has no real solutions?

Back

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

Front

What is the quadratic formula?

Back

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

Front

What is the discriminant in a quadratic equation?

Back

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.

Front

Solve for b: 5b² - 4 = 41

Back

b = 3, b = -3.

Front

What is the solution to the equation 7x² + 1 = 8?

Back

x = ±1.

Front

How do you determine the number of real solutions from a graph?

Back

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

Front

What does it mean to have two real solutions in a quadratic equation?

Back

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

Front

What is the significance of the vertex in a quadratic function?

Back

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