Solve Quadratic Equations

Front

What is the standard form of a quadratic equation?

Back

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

Front

What does the discriminant of a quadratic equation indicate?

Back

The discriminant (D = b² - 4ac) indicates the nature of the roots of the quadratic equation: if D > 0, there are 2 distinct real solutions; if D = 0, there is 1 real solution; if D < 0, there are no real solutions.

Front

Solve the quadratic equation: x² + 5x + 6 = 0

Back

x = -2, x = -3

Front

What are the roots of the equation: 2x² - 8x + 6 = 0?

Back

x = 1, x = 3

Front

If a quadratic equation has a = 1, b = -4, and c = 4, what are its roots?

Back

x = 2 (double root) because the discriminant is 0.

Front

What is the vertex form of a quadratic equation?

Back

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

Front

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

Back

The vertex (h, k) can be found using h = -b/(2a) and k = f(h), where f(x) is the quadratic function.

Front

What is the axis of symmetry for the quadratic equation y = 3x² + 6x + 2?

Back

The axis of symmetry is x = -b/(2a) = -6/(2*3) = -1.

Front

Solve the quadratic equation: x² - 4 = 0

Back

x = 2, x = -2

Front

What is the significance of the coefficient 'a' in a quadratic equation?

Back

The coefficient 'a' determines the direction of the parabola: if a > 0, it opens upwards; if a < 0, it opens downwards.