4.1-4.3 Skill Recap: Characteristics of Quadratics

Front

What is the axis of symmetry (AOS) in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror images. It can be calculated using the formula AOS = -b/2a.

Front

How do you identify the interval of increase in a quadratic function?

Back

The interval of increase is the range of x-values where the function's output (y-values) is increasing. It can be determined by analyzing the vertex and the direction of the parabola.

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point on the parabola, depending on whether it opens upwards or downwards.

Front

How do you identify the interval of decrease in a quadratic function?

Back

The interval of decrease is the range of x-values where the function's output (y-values) is decreasing. It can be determined by analyzing the vertex and the direction of the parabola.

Front

What is the standard form of a quadratic function?

Back

The standard form is given by f(x) = ax^2 + bx + c, where a, b, and c are constants.

Front

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

Back

The 'a' value determines the direction of the parabola: if 'a' is positive, the parabola opens upwards; if 'a' is negative, 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 the point (0, c) in the standard form.

Front

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

Back

The discriminant (b^2 - 4ac) determines the nature of the roots: if it's positive, there are two real roots; if zero, one real root; if negative, no real roots.

Front

How do you determine the maximum or minimum value of a quadratic function?

Back

The maximum or minimum value occurs at the vertex. For a function in standard form, it can be found by substituting the x-coordinate of the vertex back into the function.

Front

What is the vertex form of a quadratic function?

Back

The vertex form is given by f(x) = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.