Quadratic Formula and Error Analysis

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

True or False: The quadratic formula can be used for any quadratic equation regardless of its form.

Back

True

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a).

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.

Front

True or False: A quadratic equation can have at most two real solutions.

Back

True

Front

What is the vertex of a parabola represented by a quadratic equation?

Back

The vertex is the highest or lowest point of the parabola, found at the point (h, k) where h = -b/(2a) and k = f(h).

Front

What is the axis of symmetry in a quadratic function?

Back

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

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 significance of the roots of a quadratic equation?

Back

The roots (or solutions) are the x-values where the quadratic function intersects the x-axis.

Front

True or False: The quadratic formula can only be applied to equations in standard form.

Back

False; it can be applied to any quadratic equation, but it is often easiest to use when in standard form.