Quadratic Graphs & Characteristics

Front

What is the axis of symmetry in a quadratic graph?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, and it passes through the vertex.

Front

Where does the axis of symmetry pass through in a quadratic graph?

Back

The axis of symmetry passes through the vertex.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation.

Front

If a parabola has a vertex at (-3, 2), what is the equation of the axis of symmetry?

Back

x = -3.

Front

What is a parabola?

Back

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

Front

What is the standard form of a quadratic function?

Back

The standard form is f(x) = ax² + bx + c, where a, b, and c are constants.

Front

What does the 'a' value in a quadratic function determine?

Back

The 'a' value determines the direction of the parabola (upward if a > 0, downward if a < 0) and its width.

Front

What is the y-intercept of a quadratic function?

Back

The y-intercept is the point where the graph crosses the y-axis, found by evaluating f(0).

Front

How can you find the vertex of a parabola given the standard form of a quadratic function?

Back

The vertex can be found using the formula x = -b/(2a) to find the x-coordinate, then substitute back to find the y-coordinate.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b² - 4ac) determines the nature of the roots: two real roots if > 0, one real root if = 0, and no real roots if < 0.