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-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

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Page 1: -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

Page 2: -What is quadratic inequality -How to graph quadratic inequality 4-8 Quadratic Inequalities

REVIEW

Page 3: -What is quadratic inequality -How to graph quadratic inequality 4-8 Quadratic Inequalities

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.

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

GRAPH/SOLVE QUADRATIC INEQUALITIES IN…

Page 5: -What is quadratic inequality -How to graph quadratic inequality 4-8 Quadratic Inequalities

FIRST,

Page 6: -What is quadratic inequality -How to graph quadratic inequality 4-8 Quadratic Inequalities

1. HOW TO GRAPH

Page 7: -What is quadratic inequality -How to graph quadratic inequality 4-8 Quadratic Inequalities

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

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

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)

Page 9: -What is quadratic inequality -How to graph quadratic inequality 4-8 Quadratic Inequalities

Solid for y≥2x²+4x-1

Dotted for y>2x²+4x-1

Page 10: -What is quadratic inequality -How to graph quadratic inequality 4-8 Quadratic Inequalities

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

Page 11: -What is quadratic inequality -How to graph quadratic inequality 4-8 Quadratic Inequalities

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

Page 12: -What is quadratic inequality -How to graph quadratic inequality 4-8 Quadratic Inequalities

y≥2x²+4x-1

y>2x²+4x-1

Page 13: -What is quadratic inequality -How to graph quadratic inequality 4-8 Quadratic Inequalities

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

graph (the u shape)

Page 14: -What is quadratic inequality -How to graph quadratic inequality 4-8 Quadratic Inequalities

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

Dotted Line

Page 15: -What is quadratic inequality -How to graph quadratic inequality 4-8 Quadratic Inequalities

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

Dotted Line

Page 16: -What is quadratic inequality -How to graph quadratic inequality 4-8 Quadratic Inequalities

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

Solid Line

Page 17: -What is quadratic inequality -How to graph quadratic inequality 4-8 Quadratic Inequalities

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

Solid Line

Page 18: -What is quadratic inequality -How to graph quadratic inequality 4-8 Quadratic Inequalities

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

Solid Line

Dotted Line

Page 19: -What is quadratic inequality -How to graph quadratic inequality 4-8 Quadratic Inequalities

Try graphing the system

82

442

2

xxy

xxy