Quadratic Formula

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

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

Back

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

Front

What is the axis of symmetry in a parabola?

Back

The axis of symmetry is an imaginary line that divides the parabola into two mirror-image halves and passes through the vertex.

Front

Solve the quadratic equation y = -x² - 5x + 12 using the quadratic formula.

Back

The solutions are x = -6.77 and x = 1.77.

Front

Solve the quadratic equation 2x² + 2x - 12 using the quadratic formula.

Back

The solutions are x = 2 and x = -3.

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 (complex roots).

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of 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 is the highest or lowest point of the parabola, depending on its orientation.

Front

How do you find the vertex of a quadratic function in standard form?

Back

The vertex can be found using the formula: (h, k) where h = -b/(2a) and k = f(h).

Front

What is the standard form of a quadratic equation?

Back

The standard form is written as y = ax² + bx + c.