Graphing & Solving Quadratic Inequalities by 7RRk8T

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									   Graphing & Solving Quadratic
         Inequalities 5.7

What is different in the graphing process
 of an equality and an inequality?
How can you check the x-intercepts of a
 quadratic equation or inequality?
Why is it important to test 3 intervals
 after you have found the critical x
 values?
  There are four types of quadratic
    inequalities in two variables.


y > ax2 + bx + c   y < ax2 + bx + c

y ≥ ax2 + bx + c   y ≤ ax2 + bx + c
   Graphing a Quadratic Inequality in
            Two Variables
1. Draw the parabola. (Find vertex coordinates
     x=b/2a and substitute into the equation to find y.
     Then find one more point to draw the parabola.)
     Make the parabola dashed for inequalities with
     < or > and solid for inequalities with≤ or ≥.
2. Choose a point (x,y) inside the parabola and
     check whether the point is a solution of the
     inequality.
3. If the point form step 2 is a solution, shade the
     region inside the parabola. If it is not a solution,
     shade the region outside of the parabola.
y > x2 − 2x − 3

x = −b/2a=
y=
Graphing a System of Quadratic Inequalities
y ≥ x2 −4
y< −x2 −x +2

  x = −b/2a =
  y=
  x=−b/2a =
  y=
Solving a Quadratic Inequality by Graphing
          (Looking for x intercepts)
x2 − 6x + 5 < 0.
Let y = 0 and
factor to solve.

(x−1)(x−5) = 0
x = 1 or x = 5

Solution 1<x<5
  Solving a Quadratic Inequality by Graphing
2x2 + 3x− 3 ≥ 0    (Use quadratic formula to factor.)




   0.69 or −2.19
Solving a Quadratic Inequality Algebraically

  x2 + 2x ≤ 8                Test x = −5 in the equation
  x2 + 2x − 8 =0             Test x = 0 in the equation
  (x+4)(x−2)=0               Test x = 3 in the equation
  x=−4 or x=2                Solution is −4 ≤ x ≤ 2



        −4   −3    −2   −1    0    1    2
What is different in the graphing process
of an equality and an inequality?

•If the equation is > or <, the parabola is
dashed.
•Either the inside or the outside of the
parabola is shaded. Pick a point not on
the parabola and see if it makes a true
statement. If true, shade where the point
is located. If not, shade the other area.
What is different in the graphing
 process of an equality and an
 inequality?
How can you check the x-intercepts of
 a quadratic equation or inequality?
Why is it important to test 3 intervals
 after you have found the critical x
 values?
            Assignment 5.7
Page 303, 14-16, 17-45 odd,
skip 27, 39.

								
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