Intro to the Quadratic formula

Front

What is the quadratic formula?

Back

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

Front

Identify 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 does the 'a' value represent in a quadratic equation?

Back

The 'a' value represents the coefficient of x² and determines the direction of the parabola (upward if a > 0, downward if a < 0).

Front

What does the 'b' value represent in a quadratic equation?

Back

The 'b' value is the coefficient of x and affects the position of the vertex of the parabola along the x-axis.

Front

What does the 'c' value represent in a quadratic equation?

Back

The 'c' value is the constant term and represents the y-intercept of the quadratic function.

Front

How do you identify the values of a, b, and c in the equation y = 16x² - 8x - 24?

Back

In the equation y = 16x² - 8x - 24, a = 16, b = -8, and c = -24.

Front

How do you convert the equation 4x² - 8x = 3 into standard form?

Back

To convert 4x² - 8x = 3 into standard form, subtract 3 from both sides to get 4x² - 8x - 3 = 0.

Front

What is the vertex of a parabola given by the equation y = ax² + bx + c?

Back

The vertex of the parabola can be found using the formula x = -b/(2a) to find the x-coordinate, and then substituting back to find the y-coordinate.

Front

What is the discriminant in the quadratic formula?

Back

The discriminant is the part of the quadratic formula under the square root, given by b² - 4ac. It determines the nature of the roots.

Front

What does it mean if the discriminant is positive?

Back

If the discriminant is positive, the quadratic equation has two distinct real roots.