-What is quadratic inequality -How to graph quadratic inequality 4-8 Quadratic Inequalities

-What is quadratic inequality-How to graph quadratic inequality

4-8 Quadratic Inequalities

REVIEW

WHAT WE WANT TO ACHIEVE IS…

1. YOU KNOW WHAT ARE QUADRATIC INEQUALITIES.

2. YOU CAN GRAPH QUADRATIC INEQUALITIES IN TWO VARIABLES.

3. YOU CAN SOLVE QUADRATIC INEQUALITIES IN ONE VARIABLE.

4. YOU CAN SOLVE WORD QUESTIONS AND MAKE APPROPRIATE EXPRESSION WITH THE GIVEN CONDITION.

GRAPH/SOLVE QUADRATIC INEQUALITIES IN…

FIRST,

1. HOW TO GRAPH

It is similar with quadratic function…If the question asks you to graph y>2x²+4x-1, graph the related function which is y=2x²+4x-1BUT you have to consider about the parabola → solid or dotted?

STEP 1: Graph the related function

If the equation has the ≥ or ≤‘y≥2x²+4x-1’, it is solid line.(greater/less than or equal to – solid)

If the equation has the < or >‘y>2x²+4x-1’, it is dotted line.(greater/less than -dotted)

Solid for y≥2x²+4x-1

Dotted for y>2x²+4x-1

You have to test a point to decide where to shade…

Pick a point that is not on the parabola and substitute to the function! ex) y>2x²+4x-1 0>2·0²+4·0-1 → ? 0> -1 → O

So, (0,0) is a solution of the inequality.

STEP 2: Decide where to shade

Shade the right region!Since (0,0) IS the solution of the function, shade the place that contains the point.If the point you chose is NOT the solution, you should shade the place that does not contain the point.

STEP 3: Shade

y≥2x²+4x-1

y>2x²+4x-1

Graphing Quadratic Inequalitiesy=x2+4x+2 Equation – only includes the points on the

graph (the u shape)

y>x2+4x+2 –inequality – only includes the points inside the u-shape

Dotted Line

y<x2+4x+2 – inequality – only includes the points outside the parabola

Dotted Line

y≤x2+4x+2 – inequality – both outside and on the parabola

Solid Line

y≥x2+4x+2 inequality – both inside and on the parabola

Solid Line

A system – where they overlapy≥2x2 and y<-x2+1

Solid Line

Dotted Line

Try graphing the system

82

442

2

xxy

xxy