Flashcard: Sections 8.4/8.6 -Vertex Form and Properties of Quadratics

Front

What is a quadratic function?

Back

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

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.

Front

What does the 'a' value in the vertex form indicate?

Back

The 'a' value determines the direction and width of the parabola. If a > 0, the parabola opens upwards; if a < 0, it opens downwards.

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, given by the equation x = h in vertex form.

Front

How do you find the vertex of a quadratic function in standard form?

Back

To find the vertex of a quadratic function in standard form (f(x) = ax² + bx + c), use the formula h = -b/(2a) and then calculate k by substituting h back into the function.

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 f(x) = 0.

Front

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

Back

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

Front

What is exponential decay?

Back

Exponential decay describes a process where a quantity decreases at a rate proportional to its current value, often modeled by the function f(t) = a * e^(-kt), where k > 0.

Front

How can you identify a quadratic function from its graph?

Back

A quadratic function's graph is a parabola, which can open upwards or downwards and has a single vertex.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants.