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

What are the values of a, b, and c in the quadratic equation 2x² + 2x - 12 = 0?

Back

a = 2, b = 2, c = -12.

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

How do you determine the vertex of a parabola given by the equation y = ax² + bx + c?

Back

The vertex can be found using the formula: x = -b / (2a).

Front

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

Back

The discriminant indicates the nature of the roots: if > 0, two distinct real roots; if = 0, one real root; if < 0, two complex roots.

Front

Solve the quadratic equation 4x² - 8x = 3 using the quadratic formula.

Back

x = 4, x = -3.

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

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 find the x-intercepts of a quadratic function?

Back

Set y = 0 and solve the quadratic equation ax² + bx + c = 0.

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.