Question 23687
Find the vertex and intercepts for each quadratic function, and graph. 
y = -x^2 + 2x + 3 
WRITE AS A SQUARE USING X^2 AND X TERMS
Y=3-{(X^2-2*X*1+1^2)-1^2}
Y=3-(X-1)^2+1=4-(X-1)^2
SINCE (X-1)^2 IS A PERFECT SQUARE IT IS ALWAYS POSITIVE OR MINIMUM ZERO.SO WE GET A MAXIMUM VALUE FOR Y AT X=1..VALUE IS Y=4..THIS IS CALLED VERTEX.YOU CAN SEE IT IN THE GRAPH.
INTERCEPTS MEAN WHERE THE CURVE CUTS THE AXES 
PUT X=0 AND FIND Y TO GET Y INTERCEPTS..WE GET Y=3 HENCE 3 IS THE Y INTERCEPT.
PUT Y=0 AND FIND X TO GET X INTERCEPTS...WE GET 0=4-(X-1)^2
(X-1)^2=4
X-1=2....OR...X-1=-2
X=3.....OR......-1...
YOU CAN SEE IT FROM GRAPH GIVEN BELOW.
{{{ graph( 600, 600, -10, 5, -10, 10,-x^2+2x+3) }}}