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 are the values of a, b, and c in the equation 4x² - 8x = 3?

Back

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

Front

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

Back

x = -5/2, x = 7.

Front

What does the discriminant (b² - 4ac) tell us about a quadratic equation?

Back

The discriminant determines the nature of the roots: if > 0, two distinct real roots; if = 0, one real root; if < 0, no real roots.

Front

Solve using the quadratic formula: 4x² + 4x + 1 = 0

Back

x = -½.

Front

What is the standard form of a quadratic equation?

Back

The standard form is ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

How do you rearrange the equation 9x² = 4 + 7x into standard form?

Back

Rearranging gives 9x² - 7x - 4 = 0.

Front

What is the vertex form of a quadratic equation?

Back

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

Front

Solve using the quadratic formula: 2x² - x - 3 = 0

Back

x = 3/2, x = -1.

Front

What is the axis of symmetry for a quadratic equation?

Back

The axis of symmetry is given by the formula x = -b/(2a).