5-7
Solving Quadratic Inequalities
DÉJÀ VU: Graphing Linear Inequalities
Graph the inequality
The boundary line is
y-int of (0, 2) and a slope of
Draw the boundary line
dashed because it is not
part of the solution.
Then shade the region above
the boundary line to show
.
Holt Algebra 2
.
which has a
.
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Solving Quadratic Inequalities
Earlier we solved linear inequalities in two
variables by graphing. We can use a similar
procedure to graph quadratic inequalities.
Holt Algebra 2
5-7
Solving Quadratic Inequalities
Notes
1. For A) f(x)= -x2 + 7
B) f(x)= x2 + 8x - 20
C) f(x)= -2(x-3)2 +7
Identify the vertex, and state the domain and range
2. For y > (x+1)2 – 3
A. State shifts
B. Find vertex
C. Graph (and shade)
3. For y > -x2 – 4x
A. Up or downward
B. Find vertex
C. Graph (and shade)
4. For y ≤ x2 + 9x + 14
A. Up or downward
B. Find vertex
C. Find y-intercept
D. Graph (and shade)
Holt Algebra 2
5-7
Solving Quadratic Inequalities
Notes
1. Identify the vertex, state the domain and
range for A) f(x)= -x2 + 7
B) f(x)= x2 + 8x – 20
C) f(x)= -2(x-3)2 +7
2. For y = (x+1)2 – 3
A. State shifts
B. Find vertex
C. Graph y > (x+1)2 – 3
(and shade)
Holt Algebra 2
5-7
Solving Quadratic Inequalities
Example 1: Graphing Quadratic Inequalities in Two
Variables
Graph y ≥ x2 – 7x + 10.
Step 1
Holt Algebra 2
Graph the boundary
of the related parabola
y = x2 – 7x + 10 with
a solid curve. Its
y-int is (0,10), its
vertex is (3.5, –2.25).
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Solving Quadratic Inequalities
Example 1 Continued
Step 2
Holt Algebra 2
Shade above the
parabola because the
solution consists of
y-values greater than
those on the parabola
for corresponding
x-values.
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Solving Quadratic Inequalities
Example 2
Graph the inequality.
y ≥ 2x2 – 5x – 2
Step 1
Holt Algebra 2
Graph the boundary
of the related parabola
y = 2x2 – 5x – 2 with
a solid curve. Its
y-int is (0,–2), its
vertex is (1.3, –5.1).
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Solving Quadratic Inequalities
Example 2 Continued
Step 2
Holt Algebra 2
Shade above the
parabola because the
solution consists of
y-values greater than
those on the parabola
for corresponding
x-values.
5-7
Solving Quadratic Inequalities
Example 3
Graph each inequality.
y < –3x2 – 6x – 7
Step 1
Holt Algebra 2
Graph the boundary
of the related parabola
y = –3x2 – 6x – 7 with
a dashed curve. Its
y-intercept is (0, –7).
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Solving Quadratic Inequalities
Example 3 Continued
Step 2
Holt Algebra 2
Shade below the
parabola because the
solution consists of
y-values less than
those on the parabola
for corresponding
x-values.
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Solving Quadratic Inequalities
Notes
3. For y > -x2 – 4x
A. Up or downward
B. Find vertex
C. Graph (and shade)
4. For y ≤ x2 + 9x + 14
A. Up or downward
B. Find vertex
C. Find y-intercept
D. Graph (and shade)
Holt Algebra 2
5-7
Solving Quadratic Inequalities
Notes
4. For y ≤ x2 + 9x + 14
A. State whether it opens
upward or downward
B. Find the vertex
C. Find the y-intercept
D. Graph the boundary line
E. Shade
Holt Algebra 2