Quadratic Graphs

Visually, quadratic graphs are…

• parabolas

4 key features of a parabola

• opening upward/downward

• y-intercept

• vertex

• x-intercepts

What determines the direction in which a parabola opens?

• if the vertex is the maximum, the parabola opens downward

• if the vertex is the minimum, the parabola opens upward

Quadratic equation: standard form graph features

• f(x) = ax²+bx+c

• c: y-intercept

• if a is negative, parabola opens downward

• if a is positive, parabola opens upward

Quadratic equation: vertex form graph features

• f(x) = a(x-h)² + k

• h = x-coordinate of vertex

  • also the x-coordinate of the axis of symmetry

• k = y-coordinate of vertex

Quadratic Equation: Root/Zero Form Graph Features

• f(x) = a(x-n)(x-m)

• n, m = (x-coordinates of x-intercepts, or roots)

How to find the maximum or minimum value of a quadratic by graphing it

• Identify the vertex

Graph of a Quadratic with One Solution

• touches the x-axis at one singular point, which is a double root

• the vertex and the root are the same value

Graph of a Quadratic with Two Solutions

• Crosses the x-axis at two points

Graph of a Quadratic with No Solution

• Does not touch or cross the x-axis

Equation for X-coordinate of Parabolic Line of Symmetry

• x = -b/2a, taken from standard form