Quadratic Formula Rational Roots

Front

What is the Quadratic Formula?

Back

The Quadratic Formula is used to find the 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) 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 it is zero, there is one real root (a repeated root); if it is negative, there are no real roots.

Front

Solve using the Quadratic Formula: 2x² - x - 3 = 0

Back

x = 3/2 and x = -1.

Front

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

Back

x = -1 and x = -3.

Front

Solve using the Quadratic Formula: 2x² - 9x - 35 = 0

Back

x = -5/2 and x = 7.

Front

Identify the coefficients in the quadratic equation: y = x² + 5x + 7

Back

a = 1, b = 5, c = 7.

Front

Determine the values of a, b, and c for the equation: 4x² - 8x = 3

Back

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

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 vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph of a quadratic function, given by 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).