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

What does the discriminant (b² - 4ac) indicate?

Back

The discriminant determines the nature of the roots of a quadratic equation. If it is positive, there are two distinct real roots; if zero, there is one real root; if negative, there are two complex roots.

Front

Solve using the quadratic formula: 2x² + 2x - 12 = 0

Back

x = 2, x = -3.

Front

Solve using the quadratic formula: 2x² - 9x - 35 = 0

Back

x = -5/2, x = 7.

Front

Solve using the quadratic formula: 2x² + 7x - 15 = 0

Back

x = -5, x = 1.5.

Front

Identify a, b, and c in the equation: 4x² - 8x = 3

Back

a = 4, b = -8, c = -3.

Front

What is a leading coefficient in a quadratic equation?

Back

The leading coefficient is the coefficient of the term with the highest degree in a polynomial. In a quadratic equation ax² + bx + c, it is 'a'.

Front

What is the vertex of a parabola represented by a quadratic equation?

Back

The vertex is the highest or lowest point of the parabola, found at the coordinates (h, k) where h = -b/(2a) and k = f(h).

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).

Front

How do you determine if a quadratic equation has real solutions?

Back

By evaluating the discriminant (b² - 4ac). If it is greater than or equal to zero, the equation has real solutions.