12.6.24 Quadratic Review

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

How do you find the vertex of a parabola given in standard form?

Back

To find the vertex of a parabola given in standard form f(x) = ax² + bx + c, use the formula h = -b/(2a) and k = f(h).

Front

What does it mean if the vertex of a parabola is a minimum?

Back

If the vertex of a parabola is a minimum, it means the parabola opens upwards (a > 0) and the vertex is the lowest point on the graph.

Front

What does it mean if the vertex of a parabola is a maximum?

Back

If the vertex of a parabola is a maximum, it means the parabola opens downwards (a < 0) and the vertex is the highest point on the graph.

Front

How do you solve a quadratic inequality?

Back

To solve a quadratic inequality, first find the roots of the corresponding quadratic equation, then test intervals to determine where the inequality holds true.

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 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 and a ≠ 0.

Front

How can you convert a quadratic function from standard form to vertex form?

Back

To convert from standard form to vertex form, complete the square on the quadratic expression.

Front

What is the axis of symmetry in a parabola?

Back

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

Front

What is the vertex of the parabola represented by f(x) = (x + 2)² + 6?

Back

The vertex of the parabola is (-2, 6).