standard, vertex, and factored form

Front

What is the standard form of a quadratic equation?

Back

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

Front

What is the vertex form of a quadratic equation?

Back

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

Front

What is the factored form of a quadratic equation?

Back

The factored form of a quadratic equation is y = a(x - r₁)(x - r₂), where r₁ and r₂ are the roots of the equation.

Front

How do you find the vertex from the standard form?

Back

To find the vertex from the standard form y = ax² + bx + c, use the formula h = -b/(2a) and k = f(h).

Front

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

Back

The 'a' value indicates the direction of the parabola (upward if a > 0, downward if a < 0) and its width (narrower if |a| > 1, wider if |a| < 1).

Front

What is the range of a parabola that opens upwards?

Back

The range of a parabola that opens upwards is [k, ∞), where k is the y-coordinate of the vertex.

Front

What is the range of a parabola that opens downwards?

Back

The range of a parabola that opens downwards is (-∞, k], where k is the y-coordinate of the vertex.

Front

How do you determine the axis of symmetry for a parabola?

Back

The axis of symmetry for a parabola in standard form y = ax² + bx + c is x = -b/(2a).

Front

What transformation occurs when you replace f(x) with f(x) + k?

Back

The graph of the function shifts vertically by k units (up if k > 0, down if k < 0).

Front

What transformation occurs when you replace f(x) with f(x - h)?

Back

The graph of the function shifts horizontally by h units (right if h > 0, left if h < 0).