6.6 Analyzing Graphs Of Quadratic Functions

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

How can you identify the vertex of a parabola from its equation in vertex form?

Back

The vertex of a parabola in vertex form f(x) = a(x - h)² + k is (h, k).

Front

What does it mean for a parabola to open upwards or downwards?

Back

A parabola opens upwards if the coefficient 'a' is positive and downwards if 'a' is negative.

Front

How do you find the x-intercepts of a quadratic function?

Back

To find the x-intercepts, set f(x) = 0 and solve for x.

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 its orientation.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that passes through the vertex, given by the equation x = h.

Front

How do you determine if a quadratic function has a maximum or minimum value?

Back

If 'a' is positive, the function has a minimum value; if 'a' is negative, it has a maximum value.

Front

What is the formula for finding the vertex of a parabola given in standard form?

Back

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

Front

What are the roots of a quadratic function?

Back

The roots are the values of x where the function intersects the x-axis, also known as x-intercepts.

Front

What is the relationship between the discriminant and the number of real roots?

Back

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