Flashcard 11 Practice: Parts of Quadratic Functions

Front

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

Back

x = -b/(2a), where a and b are coefficients from the quadratic equation ax^2 + bx + c.

Front

What does the vertex of a quadratic function represent?

Back

The vertex is the highest or lowest point of the graph, depending on whether it opens upwards (minimum) or downwards (maximum).

Front

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

Back

If the coefficient of x^2 (a) is positive, the function has a minimum value. If a is negative, it has a maximum value.

Front

What are the x-intercepts of a quadratic function?

Back

The x-intercepts are the points where the graph crosses the x-axis, found by solving the equation ax^2 + bx + c = 0.

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 the function at x = 0.

Front

What is the standard form of a quadratic function?

Back

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

Front

What is the vertex form of a quadratic function?

Back

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

Front

How can you find the axis of symmetry from the vertex form?

Back

The axis of symmetry is the vertical line x = h, where (h, k) is the vertex.

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 positive, two real roots; if zero, one real root; if negative, no real roots.

Front

How do you find the x-intercepts using the quadratic formula?

Back

Use the quadratic formula x = (-b ± √(b^2 - 4ac)) / (2a) to find the x-intercepts.