Unit 6
The quadratic function.
The parabola up close: which way it opens, how to shift it, how many roots it has, and the vertex form.
Before this unit
The unit, lesson by lesson
Lessons
4 lessons · 12 practice questions · about an hour
The shape and sign of a
When the parabola opens upward and when it opens downward, what makes it narrow or wide, and what happens when the coefficient a passes through zero.
Shifting a parabola
How to move y = x² right, left, up and down, and how to read the vertex straight off vertex form.
Roots and the discriminant
Where the parabola crosses the x-axis, and how a single number, the discriminant, tells you in advance whether there are two roots, one or none.
From standard form to vertex form
Finding the vertex of y = ax² + bx + c, completing the square, and choosing a coefficient so that the parabola touches the axis at exactly one point.