Simplify Radicals

Front

What is a radical in mathematics?

Back

A radical is an expression that includes a root, such as a square root, cube root, etc. The most common radical is the square root.

Front

How do you simplify a radical expression?

Back

To simplify a radical expression, factor the number under the radical into its prime factors and look for pairs of factors. Each pair can be taken out of the radical.

Front

What is the square root of -1?

Back

The square root of -1 is represented by the imaginary unit 'i'.

Front

What is the quadratic formula?

Back

The quadratic formula is used to find the solutions of a quadratic equation and is given by x = (-b ± √(b² - 4ac)) / (2a).

Front

What does the discriminant in a quadratic equation tell us?

Back

The discriminant (b² - 4ac) indicates the number and type of solutions of the quadratic equation: if it's positive, there are two real solutions; if zero, one real solution; if negative, two complex solutions.

Front

How do you determine the values of a, b, and c in a quadratic equation?

Back

In the standard form of a quadratic equation ax² + bx + c = 0, 'a' is the coefficient of x², 'b' is the coefficient of x, and 'c' is the constant term.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What is the process for using the quadratic formula?

Back

To use the quadratic formula, identify the coefficients a, b, and c from the quadratic equation, substitute them into the formula, and simplify to find the values of x.

Front

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

Back

The vertex of a quadratic function is the highest or lowest point on the graph, depending on the direction of the parabola. It represents the maximum or minimum value of the function.

Front

How can you identify the direction of a parabola?

Back

The direction of a parabola can be identified by the sign of the coefficient 'a' in the quadratic equation: if 'a' is positive, the parabola opens upwards; if negative, it opens downwards.