Graphing Quadratics in Vertex Form

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

How do you identify the vertex from the equation y = 3(x + 5)² - 4?

Back

The vertex is (-5, -4). It is found by identifying h and k from the vertex form.

Front

What does the 'a' in the vertex form y = a(x - h)² + k represent?

Back

The 'a' value determines the direction and width of the parabola. If 'a' is positive, the parabola opens upwards; if negative, it opens downwards.

Front

What is the significance of the 'h' in the vertex form?

Back

The 'h' value represents the x-coordinate of the vertex and indicates the horizontal shift of the parabola.

Front

What does the 'k' in the vertex form indicate?

Back

The 'k' value represents the y-coordinate of the vertex and indicates the vertical shift of the parabola.

Front

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

Back

The axis of symmetry is the vertical line x = h, where h is the x-coordinate of the vertex.

Front

What is the y-intercept in the standard form of a quadratic equation y = ax² + bx + c?

Back

The y-intercept is the point where the graph crosses the y-axis, which occurs at (0, c).

Front

How do you convert from vertex form to standard form?

Back

Expand y = a(x - h)² + k to get y = ax² - 2ahx + (ah² + k).

Front

What is the relationship between the vertex and the minimum/maximum value of a parabola?

Back

The vertex represents the minimum value if the parabola opens upwards (a > 0) and the maximum value if it opens downwards (a < 0).

Front

How do you determine the direction of a parabola from its equation?

Back

The direction is determined by the sign of 'a': if 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.