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 square root?

Back

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

Front

What is the quadratic formula?

Back

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

Front

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

Back

It means that the graph of the quadratic does not intersect the x-axis, which occurs when the discriminant (b² - 4ac) is less than zero.

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, which determines the nature of the roots.

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 vertex of 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.

Front

How can you find the vertex of a quadratic function in standard form?

Back

The vertex can be found using the formula (-b/(2a), f(-b/(2a))) where f(x) is the quadratic function.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the equation x = -b/(2a).