9.2 Graphing Quadratic
Equations
Algebra 1
Quadratic function
• Standard form
y  ax  bx  c
2
• Every quadratic function has a U-shaped graph
called a parabola.
• Vertex is the lowest or highest pt of the parabola.
• Axis of symmetry – line passing thru the vertex,
dividing the U in half.
Graph of a Quadratic function
The graph of y  ax 2  bx  c is a parabola.
If a is positive, then the parabola opens up, U.
If a is negative, then the parabola opens down,  .
b
Half of the vertex can be found by x  2a
b
The axis of symmetry is the vertical line x  
2a
Steps to graph a quadratic f(x)
b
x
2a
• 1) Use
to find half of the vertex and
axis of symmetry.
• 2) Substitute the x value into the equation to
find the y value of the vertex.
• 3) Use the vertex to make your T-chart to find
4 other points on the parabola.
Example 1
• Solve x 2 2 x  8  0 by graphing.
• 1.) x   b
2.) Substitute
2a
•
• 3.) T-chart
Graph of Ex. 1
Ex. 2
1 2
y   x  4x  6
2
Graph of Ex. 2
Assignment
Example 1, Step 3
•
•
•
•
•
•
x l y
-2 l
-1 l
0l
1l
2l
Example 1 – Substitute each value into
the equation.
•
•
•
•
•
•
x l y
-2 l -8
-1 l
0l
1l
2l
x 2 2 x  8  y
(2) 2 2(2)  8  y
4  4  8  y
8  y
Example 1- Substitute -1
•
•
•
•
•
•
x l y
-2 l –8
-1 l –9
0l
1l
2l
x 2 2 x  8  y
(1) 2 2(1)  8  y
1  2  8  y
1  8  y
9  y
Example 1 – Substitute 0
•
•
•
•
•
•
x l y
-2 l –8
-1 l –9
0 l –8
1l
2l
x 2 2 x  8  y
0 2 2(0)  8  y
0 08  y
8  y
Example 1 – Substitute 1
•
•
•
•
•
•
x l y
-2 l –8
-1 l –9
0 l –8
1 l –5
2l
x 2 x  8  y
2
1 2 2(1)  8  y
1 2  8  y
38  y
5  y
Example 1 – Substitute 2
•
•
•
•
•
•
x l y
-2 l –8
-1 l –9
0 l –8
1 l –5
2l 0
x 2 x  8  y
2
2 2 2(2)  8  y
4 48  y
88  y
0 y
Example 1
• Did you see that we had a zero as the y value
on our last point, (2,0)? This is one of the
roots or zero’s. Once, you graph it you should
see that the parabola also crosses the x-axis at
–4. Which is the other answer we found when
factoring. I hope that you can graph this
example on graph paper to see what I am
referring to. Good Luck!
A quadratic equation…
• is an equation in which the value of the
related quadratic function is 0.
x 2 x  8  0
2
Example 1
•
•
•
•
•
Solve by Factoring
x 2 2 x  8  0
(x+4)(x-2)=0
x+4=0 x-2=0
x=-4
x=2
Roots and Zero’s
x 2 2 x  8  0
• For example,
. We have used
factoring to solve for x or the “roots”. The x
values are the x-intercepts or the “zero’s” of
the equation. They are called the “zero’s”
because the y value is zero in the ordered pair.
Let’s find the zero’s of this example.