Quadratic Graphing Characteristics

Front

What is the equation for the axis of symmetry of a quadratic function?

Back

x = -b/(2a), where the quadratic is in the form y = ax^2 + bx + c.

Front

What is the vertex of the quadratic function 2x^2 + 8x + 2?

Back

(-2, -6)

Front

What does it mean if a quadratic opens down with a maximum?

Back

The parabola has a highest point (maximum) and the coefficient of x^2 is negative.

Front

What is the standard form of a quadratic equation?

Back

y = ax^2 + bx + c.

Front

How do you find the vertex of the quadratic function y = -2x^2 + 4x + 3?

Back

The vertex is at (1, 5).

Front

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

Back

It determines the direction of the parabola (upward if a > 0, downward if a < 0).

Front

What is the formula to find the y-coordinate of the vertex?

Back

y = f(-b/(2a)) where f(x) is the quadratic function.

Front

What does the term 'discriminant' refer to in a quadratic equation?

Back

The discriminant is b^2 - 4ac and determines the nature of the roots.

Front

What are the possible values of the discriminant and their meanings?

Back

If > 0: two real roots, = 0: one real root, < 0: no real roots.

Front

What is the axis of symmetry for the function y = 3x^2 + 6x + 2?

Back

x = -1.