Quadratic Formula

Front

What is the Quadratic Formula?

Back

The Quadratic Formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the solutions of a quadratic equation ax² + bx + c = 0.

Front

What does the discriminant tell us?

Back

The discriminant (D = b² - 4ac) indicates the nature of the roots of a quadratic equation: D > 0 means two distinct real roots, D = 0 means one real root, and D < 0 means no real roots.

Front

How do you find the discriminant of the equation 4x² + 12x + 9 = 0?

Back

D = b² - 4ac = 12² - 4(4)(9) = 144 - 144 = 0.

Front

What is the first step in solving the equation x² + 6x - 13 = 3?

Back

Subtract 3 from both sides to get x² + 6x - 16 = 0.

Front

What are the roots of the equation 2x² - x - 3 = 0?

Back

The roots are x = 3/2 and x = -1.

Front

What does it mean if a quadratic equation cannot be factored?

Back

It means that the roots are either irrational or complex, and the quadratic formula should be used to find the solutions.

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

How can you determine if a quadratic equation opens upwards or downwards?

Back

If the coefficient 'a' in ax² + bx + c is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is the vertical line x = -b/(2a) that divides the parabola into two mirror-image halves.

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex represents the maximum or minimum point of the parabola, depending on whether it opens upwards or downwards.