Quadratic Formula Exit Ticket

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 (D) indicate in a quadratic equation?

Back

The discriminant D = b² - 4ac determines the nature of the roots of the quadratic equation: D > 0 means 2 real solutions, D = 0 means 1 real solution, and D < 0 means 2 imaginary solutions.

Front

If the discriminant is positive, how many solutions does the graph have?

Back

2 real solutions.

Front

If the discriminant is zero, how many solutions does the graph have?

Back

1 real solution.

Front

If the discriminant is negative, how many solutions does the graph have?

Back

2 imaginary solutions.

Front

What is a quadratic equation?

Back

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

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation (upward or downward). It can be found using the formula (-b/(2a), f(-b/(2a))).

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 equation x = -b/(2a).

Front

What does it mean for a quadratic function to open upwards?

Back

A quadratic function opens upwards if the coefficient of x² (a) is positive, indicating that the vertex is the minimum point.

Front

What does it mean for a quadratic function to open downwards?

Back

A quadratic function opens downwards if the coefficient of x² (a) is negative, indicating that the vertex is the maximum point.