PrintDay 1: Introduction to Quadratic Functions
Day 1: Introduction to Quadratic Functions
A quadratic function is defined as f(x) = ax2 + bx + c. While f(x) = mx + b produced a line, the quadratic function produces a graph which we call a parabola. A parabola is a u-shaped graph.
Parts of a Parabola from the function above:
y-intercept - where the parabola crosses the y-axis at (0, c)
vertex - the turning point of the parabola at (-b/2a, f(-b/2a))
axis-of-symmetry - the imaginary line which passes through the vertex and cuts the parabola in half at x = -b/2a
maximum - the name for the vertex when a < 0
minimum - the name for the vertex when a > 0
Recall from chapter 1 that a root is when we solve an equation equal to zero. Furthermore, recall from chapter 2 that a root is also where a graph called the x-axis. Most parabolas have two distinct roots!
Graphing
A quadratic function is defined as f(x) = ax2 + bx + c. While f(x) = mx + b produced a line, the quadratic function produces a graph which we call a parabola. A parabola is a u-shaped graph.
Parts of a Parabola from the function above:
y-intercept - where the parabola crosses the y-axis at (0, c)
vertex - the turning point of the parabola at (-b/2a, f(-b/2a))
axis-of-symmetry - the imaginary line which passes through the vertex and cuts the parabola in half at x = -b/2a
maximum - the name for the vertex when a < 0
minimum - the name for the vertex when a > 0
Recall from chapter 1 that a root is when we solve an equation equal to zero. Furthermore, recall from chapter 2 that a root is also where a graph called the x-axis. Most parabolas have two distinct roots!
Graphing
