Answer
Answers may vary
Two solutions: $y=2x^2+10x+9$ and $y=x$ ($x= -1.5, -3$)
One solution: $y=x^2+2x+1$ and $y=x+.75$ ($x=-.5$)
No solutions: $y=x^2+x+3$ and $y=x$
Work Step by Step
Two solutions:
$y=2x^2+10x+9$ and $y=x$
$2x^2+10x+9=x$
$2x^2+10x-x+9=x-x$
$2x^2+9x+9=0$
$x=(-b±\sqrt {b^2-4ac})/2a$
$x=(-9±\sqrt {9^2-4*2*9})/2*2$
$x=(-9±\sqrt {81-72})/4$
$x=(-9±\sqrt {9})/4$
$x=(-9±3)/4$
$x=(-9+3)/4$
$x=-6/4 = -1.5$
$x=(-9-3)/4$
$x=-12/4 =-3$
One solution:
$y=x^2+2x+1$ and $y=x+.75$
$x^2+2x+1=x+.75$
$x^2+2x+1-x-.75=x+.75-x-.75$
$x^2+x+.25=0$
$x=(-b±\sqrt {b^2-4ac})/2a$
$x=(-1±\sqrt {1^2-4*1*.25})/2*1$
$x=(-1±\sqrt {1-1})/2$
$x=(-1±\sqrt {0})/2$
$x=(-1±0)/2$
$x=-1/2$
No solutions:
$y=x^2+x+3$ and $y=x$
$x^2+x+3=x$
$x^2+x+3-x=x-x$
$x^2+3 =0$
$x=(-b±\sqrt {b^2-4ac})/2a$
$x=(-0±\sqrt {0^2-4*1*3})/2*1$
$x=(±\sqrt {0-12})/2$
$x=(±\sqrt {-12})/2$
We can't have the square root of a negative number, so there are no solutions.
