Graphing Quadratics

Front

What is Vertex Form of a quadratic equation?

Back

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

Front

What is Standard Form of a quadratic equation?

Back

y = ax² + bx + c, where a, b, and c are constants.

Front

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

Back

Use the formula h = -b/(2a) to find the x-coordinate, then substitute h back into the equation to find k.

Front

What is the range of a quadratic function that opens upwards?

Back

The range is y ≥ k, where k is the y-coordinate of the vertex.

Front

What is the range of a quadratic function that opens downwards?

Back

The range is y ≤ k, where k is the y-coordinate of the vertex.

Front

How can you determine if a quadratic function opens upwards or downwards?

Back

If the coefficient 'a' is positive, it opens upwards; if 'a' is negative, it opens downwards.

Front

What does the vertex of a parabola represent?

Back

The vertex is the highest or lowest point of the parabola, depending on its direction.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is the vertical line x = h, where (h, k) is the vertex.

Front

How do you convert from standard form to vertex form?

Back

Use the method of completing the square.

Front

What is the effect of changing the value of 'a' in the vertex form?

Back

Changing 'a' affects the width and direction of the parabola; larger |a| makes it narrower.