Quadratic formula Basic

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.

Front

Identify the coefficients a, b, and c in the quadratic equation: 3x² + 4x - 5 = 0.

Back

a = 3, b = 4, c = -5.

Front

What does the 'a' coefficient represent in a quadratic equation?

Back

The 'a' coefficient represents the leading coefficient, which determines the direction of the parabola (upward if a > 0, downward if a < 0).

Front

How do you find the vertex of a parabola given in standard form?

Back

The vertex can be found using the formula x = -b/(2a) to find the x-coordinate, and then substituting this value back into the equation to find the y-coordinate.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation.

Front

What is the discriminant in a quadratic equation, and what does it indicate?

Back

The discriminant is the part of the quadratic formula under the square root: b² - 4ac. It indicates the nature of the roots: if > 0, two real roots; if = 0, one real root; if < 0, no real roots.

Front

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

Back

If the coefficient 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

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 the direction it opens.

Front

How do you convert a quadratic equation from standard form to vertex form?

Back

To convert to vertex form, use the method of completing the square.

Front

What is the axis of symmetry in a quadratic function?

Back

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