Using 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 are the values of A, B, and C in the equation 10p² + 7p - 20 = 0?

Back

A = 10, B = 7, C = -20.

Front

Solve using the quadratic formula: 9x² = 4 + 7x.

Back

x = 1 or x = - \frac{4}{9}.

Front

Identify the values of A, B, and C in the equation 3m² - 14 = 11m.

Back

A = 3, B = -11, C = -14.

Front

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

Back

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

Front

Solve: 2x² + 7x - 15 = 0.

Back

x = -5 or x = 1.5.

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 y = -x² - 5x + 12 to standard form?

Back

Rearranging gives -x² - 5x + 12 = 0.

Front

What is the vertex of a parabola represented by the equation y = ax² + bx + c?

Back

The vertex can be found using the formula (-b/(2a), f(-b/(2a))).

Front

What is the axis of symmetry for a quadratic function?

Back

The axis of symmetry is the vertical line x = -b/(2a).