color(blue)"sketching " y=x^2
"given a quadratic in standard form " ax^2+bx+c
• " if " a>0" then graph is a minimum " uuu
• " if " a<0" then graph is a maximum " nnn
"the coordinates of the vertex are " (-b/(2a),f(-b/(2a)))
"the y-intercept is the value of the constant c"
"the x-intercepts are found by equating to zero"
"for " y=x^2
a>0rArruuu
"the coordinates of the vertex are " (0,0)
"the value of " c=0
"some points on the graph "
x=+-1toy=1rArr(1,1),(-1,1)
x=+-2toy=4rArr(2,4),(-2,4)" etc"
graph{x^2 [-10, 10, -5, 5]}
color(blue)"sketching " y=x^2-x-2
• " for coefficient of x " >0
"the vertex moves " -b/(2a)larr" to the left"
• " for coefficient of x " <0
"the vertex moves " -b/(2a)rarr" to the right"
y=x^2-x-2 " is the same shape as " y=x^2
"coefficient of x term is " -1
rArrx_(color(red)"vertex")=--1/(2)=1/2rarr
rArry_(color(red)"vertex")=(1/2)^2-1/2-2=-9/4
rArrcolor(magenta)"vertex "=(1/2,-9/4)
"we could find the solution to " x^2-x-2" algebraically"
"by solving " x^2-x-2=0
"However, from the graph the solutions are the values "
"of x where the graph crosses the x-axis"
"that is " x=-1" or " x=2
graph{x^2-x-2 [-10, 10, -5, 5]}
