This week in Precalculus 11, we started the Analyzing Quadratic Functions unit. We first learned about the properties of a quadratic function.

quadratic function: function that can be written in general form

general form: y = a + bx + c, where a ≠ 0

parabola: the curve of a quadratic function’s graph

vertex: a parabola’s highest (minimum) or lowest (maximum) point (if the coefficient of is positive, the vertex opens up. If it is negative, the vertex opens down)

axis of symmetry: intersects parabola at its vertex

domain: all possible x values

range: all possible y values

x-intercepts: where the parabola touches the x axis, the roots of the quadratic equation

y-intercepts: where the parabola touches the y axis.

 

Example: y = 2 + 8x + 6

x: -5, -4, -3, -2, -1, 0

y: 16, 6, 0, -2, 0, 6

vertex: (-2, -2) minimum/opens up

x-intercept: (-1, 0) & (-3, 0)

y-intercept: (0, 6)

axis of symmetry: x = -2

D: {x∈R}

R: {y ≥ -2}

 

I had not learned about many of these terms before and found it interesting that you could find so much information from the vertex.