Question

What is the solution to -5x^2+20x-17>y

Answer 1

Do you know how to complete the square?

Answer 2

no

Answer 3

Have you graphed quadratic inequalities before?

Answer 4

a long time ago

Answer 5

just try adding a number to the left side (hint: 2) and another number to the left side (hint: 2) that will just give you as adding zero which will not affect the original equation

Answer 6

If you learn to complete the square you can find the vertex of the parabola which will help you graph it.

Answer 7

1st: isolate the terms with x versus those without an x.

(-5x^2 +20x) -17 >y

2nd: Factor out the GCF of the coefficients with x.(If the leading term is negative, factor that out too.

-5(x^2-4x) -17> y

3rd: Create a perfect square by taking half of the coefficient of the 'x' term and squaring that result.

(-4/2)^2=4

4th: Put this into your expression and make sure you keep it balanced by either adding or subtracting your result to the rest of the equation.

-5(x^2-4x+4) -17 +20 > y (notice I added 20 because the 4 gets multiplied by the -5 on the outside, so to keep my problem balanced, I am going to do the opposite of adding a -20.

5th: Factor the quantity in parenthesis as a perfect square:

-5(x-2)^2+3 > y Which can be rewritten as y < -5(x-2)^2 +3

Based on this information, we know that the parabola has a vertex at (2, 3) and opens downward.

Answer 8

Also, the boundary of the parabola is dashed because the inequality is just less than.

Answer 9

Finally, to determine where to shade, just pick a test point like (0, 0) and see if the inequality is true. If it is, shade the boundary that contains (0,0). And if it is false, shade the boundary that doesn' t contain (0,0).