quadratic points

intercepts and turning points

quadratic graph properties

some of the properties of  y = x ^ 2
only considering integer points

work developed with David Wells

a ppt is here

several interesting applications of:

• straight line graphs (the chord equations are all neat)
• mid-points
• tangents (are parallel to a family of chords)
• perpendicular line equations

quadratic matching

translating y = x squared

quadratics from roots, vertex and y-intercept

parabola template and stretched graphs

which quadratic graph?

plotting a quadratic

James Tanton has several interesting quadratic graph plotting techniques
based on the vertical line of symmetry
he introduces these amongst his various you tube offerings

when sketching a quadratic, instead of completing the square he suggests factorising the non-constant terms - to easily locate two values with the same y-ordinate:

x = 0 or 5 both give y-values = 3

so the curve must be symmetrical about a vertical line mid-way between these two  x values
(at x = 2.5), enabling the lowest point (vertex) of the quadratic to be calculated

this lowest point (vertex) can also be located by considering the lowest point of  y = x(x - 5) and then translating this 3 spaces up

quadratic maximum value

what is happening in all of these questions ?

why?

a ppt is here

what is the function?
what is the maximum value?