Solving Quadratics by using the Quadratic Formula

Front

What is the Quadratic Formula?

Back

The Quadratic Formula is used to find the solutions (roots) 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) tell us about a quadratic equation?

Back

The discriminant indicates the nature of the roots of the quadratic equation: if it's positive, there are two distinct real roots; if it's zero, there is one real root (a repeated root); if it's negative, there are no real roots (the roots are complex).

Front

Solve using the Quadratic Formula: 2x² + 2x - 12 = 0

Back

x = 2 and x = -3.

Front

Identify the leading coefficient in the quadratic equation y = x² + 5x + 7.

Back

The leading coefficient is 1.

Front

Solve using the Quadratic Formula: x² + 4x - 40 = -8

Back

x = -8 and x = 4.

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of degree 2, typically in the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

Solve using the Quadratic Formula: x² + 4x + 3 = 0

Back

x = -1 and x = -3.

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

Solve using the Quadratic Formula: x² + 12x - 5 = 0

Back

x = -6 + √41 and x = -6 - √41.