Download Chapter 6, Section 2

Chapter 6, Section 2
Solving Quadratic Equations by
Graphing
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Quadratic EQUATIONS
• Quadratic FUNCTIONS take the form
y = ax2 + bx + c.
• Quadratic EQUATIONS take the form
ax2 + bx + c = 0.
• When we solve the EQUATION, we want
to find the x value that makes the value of
ax2 + bx + c equal to zero. (Graphically,
where the graph crosses the x-axis.)
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x2 - x - 6
• We can show the
value of the
quadratic
expression with a
graph:
• When does the
function equal 0?
• where the graph
crosses the x
axis.
• We call these the
roots or zeros or
solutions of the
equation.
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Three possibilities for a graph
• We can easily see that when graphing the
function y = ax2 + bx + c, one of three things will
happen:
1) The parabola will not cross the x-axis (No
Solution)
2) The parabola will JUST touch the x-axis at
one point (One Solution – Double Root)
3) The parabola will cross over the x-axis,
touching the x-axis at two points (Two
Solutions)
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Example 1
Solve x2 - 3x - 4 = 0 by graphing.
First find the axis of symmetry
using
x
b
(3)
3 3



2a
2(1)
2
2
Then we will make a table of values
with the help of symmetry.
x
y
0
1
1.5
2
3
-4
-6
-6.25
-6
-4
We see where that the solutions
are at x = -1 or 4.
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The steps to solving a quadratic
equation by graphing
1)
2)
3)
4)
5)
Write the quadratic function (Set = 0)
Find the axis of symmetry
Make a table of values
Sketch the function
See where the function crosses the xaxis -- that’s where the function
equals zero, and the equation is
solved.
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