11.21.24 Attributes of Quadratic Functions

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically written in the form f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point on the graph of a quadratic function, depending on the direction of the parabola. It can be found using the formula (-b/2a, f(-b/2a)).

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves. It can be found using the formula x = -b/2a.

Front

What are the x-intercepts of a quadratic function?

Back

The x-intercepts (or roots) are the points where the graph of the function crosses the x-axis, found by solving the equation ax² + 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, which gives the value c in the standard form.

Front

How can you determine the number of zeros of a quadratic function?

Back

The number of zeros can be determined using the discriminant (D = b² - 4ac) from the quadratic formula. If D > 0, there are 2 zeros; D = 0 means 1 zero; D < 0 means no real zeros.

Front

What does it mean if a quadratic function opens upwards?

Back

If a quadratic function opens upwards, it means the coefficient 'a' is positive (a > 0), and the vertex represents the minimum point of the graph.

Front

What does it mean if a quadratic function opens downwards?

Back

If a quadratic function opens downwards, it means the coefficient 'a' is negative (a < 0), and the vertex represents the maximum point of the graph.

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.

Front

What is the vertex form of a quadratic function?

Back

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