Solving Quadratics and Quadratic Formula

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

What is the quadratic formula?

Back

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

Front

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

Back

The discriminant indicates the nature of the roots of a quadratic equation: if it's 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 - 9x - 35 = 0

Back

x = -5/2 and x = 7.

Front

Solve: 2x² + 7x - 15 = 0

Back

x = -5 and x = 1.5.

Front

Use the quadratic formula to solve: n² = 9n - 20

Back

n = 4 and n = 5.

Front

Solve using the quadratic formula: x² + 4x - 40 = -8

Back

x = -8 and x = 4.

Front

Solve by using the quadratic formula: 7x² - 26x - 8 = 0

Back

x = 4 and x = -2/7.

Front

What is the vertex form of a quadratic equation?

Back

The vertex form of a quadratic equation is y = a(x - h)² + k, where (h, k) is the vertex of the parabola.

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 formula x = -b/(2a).