QUADRATIC GRAPHS

Front

What is a quadratic graph?

Back

A quadratic graph is a graph of a quadratic function, which is a polynomial function of degree 2, typically in the form y = ax² + bx + c.

Front

What shape does a quadratic graph form?

Back

A quadratic graph forms a parabola.

Front

What determines if a parabola opens upwards or downwards?

Back

The sign of the coefficient 'a' in the quadratic equation y = ax² + bx + c determines the direction: if 'a' is positive, it opens upwards; if 'a' is negative, it opens downwards.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on whether it opens up or down.

Front

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

Back

For a quadratic in the form y = ax² + bx + c, the vertex can be found using the formula x = -b/(2a) and then substituting x back into the equation to find y.

Front

What is the axis of symmetry in a quadratic graph?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the equation x = -b/(2a).

Front

What is the maximum or minimum value of a quadratic function?

Back

The maximum or minimum value occurs at the vertex of the parabola. If the parabola opens upwards, it has a minimum value; if it opens downwards, it has a maximum value.

Front

How can you identify the vertex from the vertex form of a quadratic equation?

Back

In the vertex form y = a(x - h)² + k, the vertex is the point (h, k).

Front

What is the significance of the 'a' value in the quadratic equation?

Back

The 'a' value affects the width and direction of the parabola: larger absolute values of 'a' make the parabola narrower, while smaller absolute values make it wider.

Front

What does it mean if a parabola has a vertex at (h, k)?

Back

It means that the point (h, k) is the highest or lowest point of the parabola, depending on its orientation.