4.52: The Quadratic Formula

Front

What is the quadratic formula?

Back

The quadratic formula is given by x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}, where a, b, and c are coefficients from the quadratic equation ax^2 + bx + c = 0.

Front

What does it mean to simplify a fraction?

Back

To simplify a fraction means to reduce it to its lowest terms, where the numerator and denominator have no common factors other than 1.

Front

What is the first step in solving the equation x^2 + 6x - 13 = 3?

Back

The first step is to subtract 3 from both sides to set the equation to zero: x^2 + 6x - 16 = 0.

Front

How do you rearrange the equation 3x^2 + 4 = -2x to use the quadratic formula?

Back

You add 2x to both sides to get 3x^2 + 2x + 4 = 0.

Front

What is the significance of the discriminant in the quadratic formula?

Back

The discriminant, given by b^2 - 4ac, determines the nature of the roots of the quadratic equation: if it's positive, there are two real roots; if zero, one real root; if negative, two complex roots.

Front

How do you identify the coefficients a, b, and c in the quadratic equation ax^2 + bx + c = 0?

Back

In the equation, a is the coefficient of x^2, b is the coefficient of x, and c is the constant term.

Front

What is the solution to the equation r^2 = -49?

Back

The solution is r = \pm 7i, where i is the imaginary unit.

Front

What does it mean to plug in values into the quadratic formula?

Back

Plugging in values means substituting the coefficients a, b, and c from the quadratic equation into the quadratic formula to find the values of x.

Front

What is the first step in solving a quadratic equation using the quadratic formula?

Back

The first step is to rearrange the equation into the standard form ax^2 + bx + c = 0.

Front

What is the role of the square root in the quadratic formula?

Back

The square root in the quadratic formula is used to find the values of x that satisfy the equation, specifically to calculate the roots based on the discriminant.