How do you solve this equation y>3x²-8x

Question

I'm a lost parent trying to help by 10th grader with her math homework.

additional problems

y>x²-5x

y<-6x²+2x+3

y< 5x² + 2x - 6

Answer 1

for these problems you want to graph the parabola y=ax^2 +bx +c

It will U shaped if a>0 and upside down U shaped if a<0

if it is < or > rather than <= or >= then the graph is dotted to indicate that the parabola itself is not part of the solution

you will then be shading in either below or  above the parabola

checking whether (0,0) is part of the solution or not ; it is an easy check whether you have shaded the correct region

for y>3x^2-8x

y>x(3x-8)

the graph crosses the x-axis at (0,) and (8/3,0); it is U shaped

you can plot a few more points for accuracy, dot in the parabola, shade above

same for y>x^2-5x =x(x-5)

goes through (0,0) and (5.0), vertex (bottom of graph is (2.5, -6.25)

dotted line, U-shaped, shade above

the third  graph is an inverted U, dotted, shade inside and below the parabola

-(6x^2 -2x-3) this doesn't factor so plot some points