Quadratic Models

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Key Skills

Quadratic Models

SL AI 2.5

A quadratic model has a turning point (vertex) at which its minimum or maximum value occurs. The general form of a quadratic equation is ax2+bx+c.

If a<0, the turning point of a quadratic is its maximum; if a>0, the turning point of a quadratic is its minimum.

Quadratic x-intercepts

SL AI 2.5

The roots of a quadratic correspond to the x-intercepts of its graph. When x=a or x=β, the entire expression equals zero, which is reflected on the graph.

The equation of the parabola below is −(x−α)(x−β):

Vertex and Axis of Symmetry

SL AI 2.5

The graph of a quadratic function has the general shape of a parabola.

It is symmetrical about the axis of symmetry and has a maxima or minima at the vertex, which lies on the axis of symmetry.

Quadratic Models

SL AI 2.5

A quadratic model has a turning point (vertex) at which its minimum or maximum value occurs. The general form of a quadratic equation is ax2+bx+c.

If a<0, the turning point of a quadratic is its maximum; if a>0, the turning point of a quadratic is its minimum.

Quadratic x-intercepts

SL AI 2.5

The roots of a quadratic correspond to the x-intercepts of its graph. When x=a or x=β, the entire expression equals zero, which is reflected on the graph.

The equation of the parabola below is −(x−α)(x−β):

Vertex and Axis of Symmetry

SL AI 2.5

The graph of a quadratic function has the general shape of a parabola.

It is symmetrical about the axis of symmetry and has a maxima or minima at the vertex, which lies on the axis of symmetry.