Graphing Quadratics in Vertex Form

Front

What is the vertex form of a quadratic equation?

Back

The vertex form of a quadratic equation is given by y = 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 of the parabola (upward if a > 0, downward if a < 0) and the width of the parabola (narrower if |a| > 1, wider if |a| < 1).

Front

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

Back

The axis of symmetry can be found using the formula x = h, where (h, k) is the vertex of the parabola.

Front

What is the vertex of the parabola given by the equation y = 2(x + 3)² - 5?

Back

The vertex is (-3, -5).

Front

What is the significance of the axis of symmetry in a parabola?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves.

Front

How do you convert from standard form to vertex form?

Back

To convert from standard form (y = ax² + bx + c) to vertex form, complete the square.

Front

What are the x-intercepts of the parabola y = (x - 2)(x + 4)?

Back

The x-intercepts are x = 2 and x = -4.

Front

What is the general shape of a parabola?

Back

A parabola is a U-shaped curve that can open upwards or downwards.

Front

What is the formula for finding the vertex from the standard form of a quadratic equation?

Back

The vertex (h, k) can be found using h = -b/(2a) and k = f(h), where f(x) is the quadratic function.

Front

What does it mean if a parabola has no real roots?

Back

If a parabola has no real roots, it means that the graph does not intersect the x-axis, indicating that the discriminant (b² - 4ac) is less than zero.