Quadratic Characteristics Review

Front

What is the equation of the axis of symmetry for a parabola?

Back

The equation of the axis of symmetry is given by x = -b/(2a) for the quadratic equation y = ax^2 + bx + c.

Front

If a > 0 in the equation y = ax^2 + bx + c, what can we say about the graph of the parabola?

Back

The graph of the parabola will open upwards.

Front

What is the axis of symmetry for the quadratic equation y = 3x^2 - 6x + 4?

Back

The axis of symmetry is x = 1.

Front

How do you determine the vertex of a quadratic equation in standard form?

Back

The vertex can be found using the formula (h, k) where h = -b/(2a) and k = f(h).

Front

What happens to the graph of a quadratic when the c value in y = ax^2 + bx + c is changed?

Back

Changing the c value transforms the graph up and down.

Front

What is the vertex of the quadratic equation y = x^2 - 9x + 20?

Back

The vertex is (4.5, -0.25).

Front

What does the term 'parabola' refer to in mathematics?

Back

A parabola is a U-shaped curve that represents the graph of a quadratic function.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is y = ax^2 + bx + c.

Front

What does the coefficient 'a' indicate about the direction of a parabola?

Back

If a > 0, the parabola opens upwards; if a < 0, it opens downwards.

Front

How can you find the y-intercept of a quadratic function?

Back

The y-intercept can be found by evaluating the function at x = 0, which gives y = c.